فهرست مطالب

Bulletin of Iranian Mathematical Society - Volume:43 Issue:7, 2018
  • Volume:43 Issue:7, 2018
  • تاریخ انتشار: 1396/11/20
  • تعداد عناوین: 40
|
  • Existence of ground state solutions for a class of nonlinear elliptic equations with fast increasing weight
    L. Li, C.-L. Tang * Pages 2111-2124
    This paper is devoted to get a ground state solution for a class of nonlinear elliptic equations with fast increasing weightý. ýWe apply the variational methods to prove the existence of ground state solutioný.
    Keywords: Self, similar solution?, ?variational methods?, ?ground state solution?
  • The ranks of the classes of A10
    A.B.M?. Basheer * Pages 2125-2135
    ýLet G be a finite group and X be a conjugacy class of G. Theý ýrank of X in G, denoted by rank(G:X), is defined toý ýbe the minimal number of elements of X generating G. In thisý ýpaper we establish the ranks of all the conjugacy classes ofý ýelements for simple alternating group A10 using the structureý ýconstants method and other results established iný ý[A.B.Mý. ýBasheer and Jý. ýMooriý, ýOn the ranks of the alternating group Aný, ýBullý. ýMalaysý. ýMathý. ýSciý. ýSoc..
    Keywords: Conjugacy classes, rank, generation, structure constant, alternating group
  • H. Ghayour, A. Erfanian *, A. Azimi, M. Farrokhi D. G Pages 2137-2152
    We generalize the notion of Jacobson graphs into n-array columns called n-array Jacobson graphs and determine their connectivities and diameters. Also, we will study forbidden structures of these graphs and determine when an n-array Jacobson graph is planar, outer planar, projective, perfect or domination perfect.
    Keywords: Jacobson graph?, ?connectivity?, ?planar graph?, ?outer planar graph?, ?perfect graph?
  • E. Khojastehnezhad, M. Bidkham * Pages 2153-2167
    ýLet p(z) be a polynomial of degree n and for a complex number αý, ýlet Dαp(z)=np(z)(α−z)p′(z) denote the polar derivative of the polynomial p(z) with respect to αý. ýDewan et al provedý ýthat if p(z) has all its zeros in |z|≤k, (k≤ýý1), with s-fold zeros at the origin then for everyý ýα∈C with |α|≥ký,
    ýýmax|z|=1|Dαp(z)|≥ýý(n)(|α|−k)1鉦|z|=1|p(z)|ý.ý
    In this paperý, ýwe obtain a refinementý ýof above inequalityý. ýAlso as an application of our resultý, ýwe extend some inequalities forý ýpolar derivative of a polynomial of degree n whichý ýdoes not vanish in |z|
    Keywords: Polynomial?, ?inequality?, ?maximum? ?modulus?, ?polar derivative?, ?restricted zeros?
  • Y. Mao *, X. Ma, X. Tang, J. Huang Pages 2169-2182
    ýLet τ be a subgroup functor and H a p-subgroup of a finite group Gý. ýLet G¯=G/HG and H¯=H/HGý. ýWe say that H is Φ-τ-quasinormal in G if for some S-quasinormal subgroup T¯ of G¯ and some τ-subgroup S¯ of G¯ contained in H¯ý, ýH¯T¯ is S-quasinormal in G¯ and H¯∩T¯≤S¯Φ(H¯)ý. ýIn this paperý, ýwe study the structure of a group G under the condition that some primary subgroups of G are Φ-τ-quasinormal in Gý. ýSome new characterizations about p-nilpotency and solubility of finite groups are obtained.
    Keywords: S, quasinormal subgroups, p, nilpotent subgroups?, ?subgroup functor, soluble group?
  • Linear codes with complementary duals related to the complement of the Higman-Sims graph
    B.G. Rodrigues * Pages 2183-2204
    ýIn this paper we study codes Cp(HiS¯¯¯¯¯¯¯¯) where p=3,7ý,ý11 defined by the 3ý- ý7ý- ýand 11-modular representations of the simple sporadic group HS of Higman and Sims of degree 100ý. ýWith exception of p=11 the codes are those defined by the row span of the adjacency matrix of the complement of the Higman-Sims graph over GF(3) and GF(7). We show that these codes have a similar decoding performance to that of their binary counterparts obtained from the Higman-Sims graphý. ýIn particularý, ýwe show that these are linear codes with complementary dualsý, ýand thus meet the asymptotic Gilbert-Varshamov boundý. ýFurthermoreý, ýusing the codewords of weight 30 in Cp(HiS¯¯¯¯¯¯¯¯) we determine a subcode of codimension 1ý, ýand thus show that the permutation module of dimension 100 over the fields of 3ý, ý7 and 11-elementsý, ýrespectively is the direct sum of three absolutely irreducible modules of dimensions 1ý, ý22 and 77ý. ýThe latter being also the subdegrees of the orbit decomposition of the rank-3 representationý.
    Keywords: Strongly regular graph?, ?Higman, Sims graph?, ?linear code?, ?automorphism group?
  • A.A. Estaji, A. Karimi Feizabad, M. Zarghani * Pages 2205-2226
    ýIn this paperý, ýwe define and study the notion of zero elements in topoframes; a topoframe is a pairý ý(Lý,ýτ)ý, ýabbreviated Lτý, ýconsisting of a frame L and aý ýsubframe τ all of whose elements are complemented elements iný ýLý. ýWe show thatý ýthe f-ring R(Lτ)ý, ýthe set of τ-real continuous functions on Lý, ýis uniformly completeý. ýAlsoý, ýthe set of all zero elements in a topoframeý ýis closed under the formation of countable meets and finite joinsý. ýAlsoý, ýwe introduce the notion of z-filters and z-ideals in modified pointfree topologyý ýand make ready some results about themý.
    Keywords: Topoframe?, ?zero element?, ?z, filter?, ?z, ideal?, ?prime ideal
  • O. Tasdemir *, F. Karabacak Pages 2227-2231
    ýA module M is called FI-extending if every fully invariant submodule of M is essential in a direct summand of Mý. ýIt is not known whether a direct summand of an FI-extending module is also FI-extendingý. ýIn this studyý, ýit is given some answers to the question that under what conditions a direct summand of an FI-extending module is an FI-extending module?
    Keywords: Extending module?, ?direct summand?, ?left exact preradical?
  • I.P. Debnath *, S.K. Gupta Pages 2233-2258
    ýIn this articleý, ýwe formulate two dual models Wolfe and Mond-Weir related to symmetric nondifferentiable multiobjective programming problemsý. ýFurthermoreý, ýweaký, ýstrong and converse duality results are established under K-Gf-invexity assumptionsý. ýNontrivial examples have also been depicted to illustrate the theorems obtained in the paperý. ýResults established in this paper unify and extend some previously known results appeared in the literature
    Keywords: Multiobjective programming?, ?K, Gf, invexity?, ?support function?, ?efficient solutions?, ?duality?
  • G.W. Chang, H. Kim * Pages 2259-2267
    ýLet D be an integral domain with quotient field Ký, ýE be a K-vector spaceý, ýR=D∝E be the trivial extension of D by Eý, ýand w be the so-called w-operationý. ýIn this paperý, ýwe show thatý ýR is a w-FF ring if and only if D is a w-FF domain; andý ýin this caseý, ýeach w-flat w-ideal of R is w-invertible.
    Keywords: w, flat module?, ?w, FF ring?, ?trivial extension?
  • E. Akalan, B. Sarac Pages 2269-2274
    In this paper we investigate the sufficiency criteria which guarantee the classical localization of a bounded ring at its prime ideals.
    Keywords: Localizationý, ýprojective idealý, ýeventuallyý ýidempotent idealý, ýbounded rings
  • T. Beberok * Pages 2275-2280
    ýIn this paper we investigate a two classes of domains in Cn generalizing the Hartogs triangleý. ýWe prove optimal estimates for the mapping properties of the Bergman projection on these domains.
    Keywords: Hartogs triangle?, ?Bergman projection?, ?Bergman kernel
  • I. Javaid *, M. Murtaza, M. Asif, F. Iftikhar Pages 2281-2292
    ýA set of vertices S of a graph G is called a fixing set of Gý, ýif only the trivial automorphism of G fixes every vertex in Sý. ýThe fixing number of a graph is the smallest cardinality of a fixingý ýsetý. ýThe fixed number of a graph G is the minimum ký, ýsuch that ýevery k-set of vertices of G is a fixing set of Gý. ýA graph Gý ýis called a k-fixed graphý, ýif its fixing number and fixed numberý ýare both ký. ýIn this paperý, ýwe study the fixed number of a graphý ýand give a construction of a graph of higher fixed number from aý ýgraph of lower fixed numberý. ýWe find the bound on k in terms ofý ýthe diameter d of a distance-transitive k-fixed graphý.
    Keywords: Fixing set?, stabilizer?, fixing number?, fixed number?
  • G. Muhiuddin *, A.M. Al-Roqi, S. Aldhafeeri Pages 2293-2306
    ýThe notion of (Boolean) uni-soft filtersý ýin MTL-algebras is introducedý, ýand several properties of them areý ýinvestigatedý. ýCharacterizations of (Boolean) uni-soft filters are discussedý, ýand some (necessary and sufficient) conditionsý ýfor a uni-soft filter to be Boolean are providedý.
    ýThe condensational property for a Boolean uni-soft filter is established.
    Keywords: MTL, algebras?, ?(Boolean) filter?, ?(Boolean) uni, soft filter?
  • M. Avdispahic, Z. Sabanac * Pages 2307-2321
    ýBy observing the equivalence of assertions on determining the jump of aý ýfunction by its differentiated or integrated Fourier seriesý, ýwe generalize aý ýprevious result of Kvernadzeý, ýHagstrom and Shapiro to the whole class ofý ýfunctions of harmonic bounded variationý. ýThis is achieved without the finiteness assumption oný ýthe number of discontinuitiesý. ýTwo results on determination of jumpý ýdiscontinuities by means of the tails of integrated Fourier-Chebyshev series are also derived.
    Keywords: Fourier series?, ?generalized bounded variation?, ?jump discontinuities?
  • L. Zou * Pages 2323-2326
    In this short note, we present a refinement of the logarithmic-geometric mean inequality. As an application of our result, we obtain an operator inequality associated with geometric and logarithmic means.
    Keywords: Taylor's Theorem, logarithmic mean, geometric mean, operator inequality
  • S. Jafari, H. Sharifi * Pages 2327-2337
    A finite group G is called rational if all its irreducible complex characters are rational valued. In this paper we discuss about rational groups with Sylow 2-subgroups of nilpotency class at most 2 by imposing the solvability and nonsolvability assumption on G and also via nilpotency and nonnilpotency assumption of G.
    Keywords: Rational group, nilpotency class, Markel group
  • G.-Z. Ma * Pages 2339-2347
    ýWe prove that the historic set for ratioý ýof Birkhoff average is either empty or full of Hausdorff dimension in a class of one dimensionalý ýnon-uniformly hyperbolic dynamical systems.
    Keywords: Historic set?, ?Moran set?, ?non, uniformly hyperbolic?
  • M. Abdullahi Rashid, B. Mashayekhy *, H. Torabi, S. Z. Pashaei Pages 2349-2370
    ýIn this paperý, ýwe are interested in studying subgroups of topologized fundamental groups and their influences on generalized covering mapsý.
    ýMore preciselyý, ýwe find some relationships between generalized covering subgroups and the other famous subgroups of the fundamental group equipped with the compact-open topology and the whisker topologyý. ýMoreoverý, ýwe present some conditions under which generalized coveringsý, ýsemicoverings and coverings are equal.
    Keywords: Generalized covering?, ?quasitopological fundamental group?, ?whisker topology?, ?semilocally small generated?, ?homotopically Hausdorff?
  • X.F. Hu, X.B. Li * Pages 2371-2381
    ýIn this paperý, ýwe study the Hölder continuity of solution mapping to a parametric variational inequalityý. ýAt firstý, ýrecalling a real-valued gap function of the problemý, ýwe discuss the Lipschitz continuity of the gap functioný. ýThen under the strong monotonicityý, ýwe establish the Hölder continuity of the single-valued solution mapping for the problemý. ýFinallyý, ýwe apply these results to a traffic network equilibrium problem.
    Keywords: Holder continuity, gap function, parametric variational inequality, traffic network equilibrium problem
  • S. Ayad * Pages 2383-2392
    In this paper, a new approach is applied to study the self-similar solutions of 2×2 systems of nonlinear hyperbolic conservation laws. A notion of characteristic directions is introduced and then used to construct local and smooth solutions of the associated Riemann problem
    Keywords: Self, similar solutions, Riemann problem, Hyperbolic conservation laws, Smooth solutions
  • P. Chen * Pages 2393-2410
    ýIn this paperý, ýwe study the Neumann boundary value problem of a class of nonlinear divergence type diffusion equationsý. ýBy a priori estimatesý, ýdifference and variation techniquesý, ýwe establish the existence and uniqueness of weak solutions of this problem.
    Keywords: Existence, uniqueness, weak solution, variation problem, N, function
  • H. Arabyani * Pages 2411-2418
    ýIn this paperý, ýwe study the Neumann boundary value problem of a class of nonlinear divergence type diffusion equationsý. ýBy a priori estimatesý, ýdifference and variation techniquesý, ýwe establish the existence and uniqueness of weak solutions of this problem.
    Keywords: Pair of Lie algebras, Schur multiplier, c, nilpotent multiplier
  • M. Mojahedfar, A. Tari Marzabad * Pages 2419-2435
    ýIn this paperý, ýwe introduce the two-dimensional Legendre wavelets (2D-LWs)ý, ýand develop them for solving a class of two-dimensional integro-differential equations (2D-IDEs) of fractional orderý. ýWe also investigate convergence of the methodý. ýFinallyý, ýwe give some illustrative examples to demonstrate the validity and efficiency of the method.
    Keywords: Two, dimensional integro, differential equations?, fractional operators?, ?Legendre wavelets?, operational matrix?
  • S. Babaie-Kafaki *, R. Ghanbari Pages 2437-2448
    Using search directions of a recent class of three--term conjugate gradient methods, modified versions of the Hestenes-Stiefel and Polak-Ribiere-Polyak methods are proposed which satisfy the sufficient descent condition. The methods are shown to be globally convergent when the line search fulfills the (strong) Wolfe conditions. Numerical experiments are done on a set of CUTEr unconstrained optimization test problems. They demonstrate efficiency of the proposed methods in the sense of the Dolan-More performance profile.
    Keywords: Unconstrained optimization?, ?conjugate gradient method?, ?sufficient descent property?, ?line search?, ?global convergence?
  • S.H. Rasouli * Pages 2449-2455
    ýWe present a Picone's identity for theý ýAp(x)-Laplacianý, ýwhich is an extension of the classicý ýidentity for the ordinary Laplaceý. ýAlsoý, ýsome applications of ourý ýresults in Sobolev spaces with variable exponent are suggested.
    Keywords: Picone's identity, mathcalAp(x), Laplacian, Nonlinear elliptic problems?
  • A.R. Alehafttan, N. Shirali * Pages 2457-2470
    ýIn this articleý, ýwe firstý ýshow that non-Noetherian Artinian uniserial modules overý ýcommutative ringsý, ýduo ringsý, ýfinite R-algebras and rightý ýNoetherian rings are 1-atomic exactly like Zp∞ý. ýConsequentlyý, ýwe show that if R is a right duo (orý, ýa rightý ýNoetherian) ringý, ýthen the Noetherian dimension of an Artinianý ýmodule with homogeneous uniserial dimension is less than or equalý ýto 1ý. ýIn particularý, ýif A is a quotient finite dimensionalý ýR-module with homogeneous uniserial dimensioný, ýwhere R is aý ýlocally Noetherian (orý, ýa Noetherian duo) ringý, ýthen n-dim ýA≤ýý1ý. ýWe also show that the Krull dimension of Noetherian modules isý ýbounded by the uniserial dimension of these modulesý. ýMoreoverý, ýwe introduce the concept of qu-uniserial modules and by using thisý ýconceptý, ýwe observe that if A is an Artinian R-moduleý, ýsuch thatý ýany of its submodules is qu-uniserialý, ýwhere R is a right duo (orý, ýa right Noetherian) ringý, ýthen n-dim ýA≤1.
    Keywords: Noetherian dimension, homogeneous uniserial dimension, atomic modules
  • S. Alikhani *, S. Soltani Pages 2471-2482
    ýThe distinguishing number (resp. index) D(G) (D′(G)) of a graph G is the least integer dýýsuch that G has an vertex labeling (resp. edge labeling) with d labels that is preserved only by a trivialý ýautomorphismý. ýFor any n∈Ný, ýthe n-subdivision of G is a simple graph G1n which is constructed by replacing each edge of G with a path of length ný.
    ýThe mth power of Gý, ýis a graph with same set of vertices of G and an edge between two vertices if and only if there is a path of length at most m between them in G.ý
    ý The fractional power of Gý, ýis the mth power of the n-subdivision of Gý, ýi.e.ý, ý(G1n)m or n-subdivision of m-th power of Gý, ýi.e.ý, ý(Gm)1ný. ýIn this paper we study the distinguishing number and the distinguishing index of the natural and the fractional powers of Gý. ýWe show that the natural powers more than one of a graph are distinguished by at most three edge labelsý. ýWe also show that for a connected graph G of order n⩾3 with maximum degree Δ(G)ý, ýand for k⩾2ý, ýD(G1k)⩽⌈Δ(G)−−−−−√k⌉ý. ýFinally we prove that for m⩾2ý, ýthe fractional power of Gý, ýi.e.ý, ý(G1k)m and (Gm)1k are distinguishedý ý by at most three edge labelsý.
    Keywords: Distinguishing index?, ?distinguishing number?, ?fractional power?
  • H. Momenaee Kermani *, M. Ashenab Pages 2483-2493
    ýIn wireless communication systemsý, ýspace-time codes are applied to encode data when multiple antennas are used in the receiver and transmitterý. ýThe concept of diversity is very crucial in designing space-time codesý. ýIn this paperý, ýusing the equivalent definition of full diversity space-time codesý, ýwe first characterize all real and complex 2×2 rate one linear dispersion space-time block codes that are full diversityý. ýThis characterization is used to construct full diversity codes which are not derived from Alamouti schemeý. ýThený, ýwe apply our results to characterize all real subspaces of M2(C) and M2(R) whose nonzero elements are invertibleý. ýFinallyý, ýfor any natural number n>1ý, ýwe construct infinitely many inequivalent subspaces of Mn(C) whose nonzero elements are invertible.
    Keywords: Space, time coding?, ?linear dispersion?, ?full diversity?, ?full rank?
  • E. Ansari-Piri, R.G. Sanati *, M. Kardel Pages 2495-2505
    ýIn this paperý, ýwe characterize the class of orthogonality preserving operators on an infinite-dimensional Hilbert space H as scalar multiples of unitary operators between H and some closed subspaces of Hý. ýWe show that any circle (centered at the origin) is the spectrum of an orthogonality preserving operatorý. ýAlsoý, ýwe prove that every compact normal operator is a strongly orthogonality preserving operatorý.
    Keywords: Orthogonality preserving operators?, ?adjoint of operators?, isometry?, unitary operators?
  • J. Ren * Pages 2507-2516
    ýLet R be a ringý ýwith the Jacobson radical J(R) and let π:R→R/J(R) beý the canonical mapý. ýThen π induces an order preserving group homomorphismý ýK0π:K0(R)→K0(R/J(R)) and aný ýaffine continuous map S(K0π) between the state space St(R/J(R)) and theý ýstate space St(R).ý ýIn this paperý, ýwe consider the natural affine map S(K0π). We give a condition under which S(K0π) isý ýan affine homeomorphismý. ýAt the same timeý, ýwe discuss the relationship between semilocal rings and semiperfect rings by using theý ýaffine map S(K0π).
    Keywords: State space?, ???(K0)?? group?, ?pre, ordered group?, ?affine map?
  • T. Feng, M. Yu * Pages 2517-2530
    In this paper, we derive a nonlinear Picone identity to the pseudo p-Laplace operator, which contains some known Picone identities and removes a condition used in many previous papers. Some applications are given including a Liouville type theorem to the singular pseudo p-Laplace system, a Sturmian comparison principle to the pseudo p-Laplace equation, a new Hardy type inequality with weight and remainder term, a nonnegative estimate of the functional associated to pseudo p-Laplace equation.
    Keywords: Nonlinear Picone identity?, ?pseudo p, Laplace equation?, ?pseudo p, Laplace system?
  • N. Mohammadi Jouzdani, S. Mahmoodi *, A. Parvardeh Pages 2531-2545
    ýIn this paper we provide sufficient condition for existence of aý ýunique Hilbert valued (H-valued) periodicallyý ýcorrelated solution to the first order autoregressive modelý ýXn=ρnXn−1ý, ýfor \ n∈Zý, ýandý ýformulate the existing solution and its autocovariance operatorý. ýAlso we specially investigate equivalent condition for theý ýcoordinate process ⟨Xn,v⟩ý, ýforý ýarbitrary element v in Hý, ýto satisfy in someý ýautoregressive modelý. ýFinallyý, ýwe extend our result to theý ýautoregressive process with finite orderý.
    Keywords: Second order process?, autoregressive process?, periodically correlated process?, ?Hilbert valued process?, linear? ?operator?
  • R. Shukla *, R. Pant, Z. Kadelburg, H. Nashine Pages 2547-2565
    ýWe present some existence and convergence results for a general class of nonexpansive mappings in partially ordered hyperbolic metric spacesý. ýWe also give some examples to show the generality of the mappings considered herein.
    Keywords: Hyperbolic metric space?, ?nonexpansive mapping?, ?condition (C)
  • S.H. Jafari * Pages 2567-2576
    ýLet G be a finite p-group of order pn andý ý|M(G)|=p12n(n−1)−t(G)ý, ýwhere M(G)ý ýis the Schur multiplier of G and t(G) is a nonnegative integerý. ýThe classification of such groups G is already known for t(G)≤ýý6ý. ýThis paper extends the classification to t(G)=7.
    Keywords: Schur multiplier, Nonabelian tensor square, p, Group
  • H. Khabazian * Pages 2577-2583
    ýIn this paper we give conditions under which a ring is isomorphic to a structural matrix ring over a division ring.
    Keywords: Duo?, ?artinian?, ?distributive?, ?uniserial?, ?structural matrix?
  • H.M. Ahmed * Pages 2585-2615
    Suppose that for an arbitrary function f(x,y) of two discrete variables, we have the formal expansions. [f(x,y)=sumlimits_{m,n=0}^{infty }a_{m,n},P_{m}(x)P_{n}(y),]
    ýýxmPj(x)=∑n=02mam,n(j)Pj−n(x)ý,
    ýwe find the coefficients b(p,q,ℓý,ýr)i,j in the expansioný
    ýýxℓyr∇px∇qyf(x,y)=xℓýýyrf(p,q)(x,y)=∑m,n=0∞ýýa(p,q)m,nPm(x)Pn(y),a(0,0)m,n=am,ný,
    ýWe give applications of these results in solving partial differenceý ýequations with varying polynomial coefficientsý, ýby reducing them toý ýrecurrence relations (difference equations) in the expansioný ýcoefficients of the solutioný.
    Keywords: ?Hahn?, ?Meixner?, ?Kravchuk, Charlier? ?polynomials, expansion coefficient, recurrence relations, linear? ?difference equations, connection coefficients
  • K. Emir *, S. Cetin Pages 2617-2634
    ýWe firstly prove the completeness of the category of crossed modules in a modified category of interestý. ýAfterwardsý, ýwe define pullback crossed modules and pullback cat objects that are both obtained by pullback diagrams with extra structures on certain arrowsý. ýThese constructions unify many corresponding results for the cases of groupsý, ýcommutative algebras and can also be adapted to various algebraic structuresý.
    Keywords: Modified category of interest?, ?crossed module?, ?cat object?, ?limit?
  • A. Rastegar * Pages 2635-2653
    ýThe concept of self-similarity on subsets of algebraic varietiesý ýis defined by considering algebraic endomorphisms of the varietyý ýas `similarity' mapsý. ýSelf-similar fractals are subsets of algebraic varietiesý ýwhich can be written as a finite and disjoint union ofý ý`similar' copiesý. ýFractals provide a framework in whichý, ýone caný ýunite some results and conjectures in Diophantine geometryý. ýWeý ýdefine a well-behaved notion of dimension for self-similar fractalsý. ýWe alsoý ýprove a fractal version of Roth's theorem for algebraic points oný ýa variety approximated by elements of a fractal subsetý. ýAs aý ýconsequenceý, ýwe get a fractal version of Siegel's theorem on finiteness of integral pointsý ýon hyperbolic curves and a fractal version of Falting's theorem ýon Diophantine approximation on abelian varietiesý.
    Keywords: Self, similarity, Diophantine approximation, arithmetic dynamics
  • L. Meng * Pages 2655-2662
    Let complex matrices A and B have the same sizes. Using the singular value decomposition, we characterize the g-inverse B(1) of B such that the distance between a given g-inverse of A and the set of all g-inverses of the matrix B reaches minimum under the unitarily invariant norm. With this result, we derive additive and multiplicative perturbation bounds of the nearest perturbed g-inverse. These results generalize and improve the existing results published recently to some extent.
    Keywords: g, inverse, additive perturbation bound, multiplicative perturbation bound, unitarily invariant norm