Bulletin of Iranian Mathematical Society
Volume:41 Issue: 6, 2015

‎We consider the uniqueness problem of algebroid functions‎ ‎on an angular domain‎. ‎Several theorems are established to extend the uniqueness theory of meromorphic functions to algebroid functions‎.

‎The objective of this paper is to obtain an upper bound to the second Hankel determinant |a 2 a 4 −a 2 3 | |a2a4−a32| ‎for the function f f‎, ‎belonging to the class of Gamma-starlike functions‎, ‎using Toeplitz determinants‎. ‎The result presented here include‎ ‎two known results as their special cases‎.

‎A total dominating set of a graph G G is a set D D of vertices of G G such that every vertex of G G has a neighbor in D D ‎. ‎The total domination number of a graph G G ‎, ‎denoted by γ t (G) γt(G) ‎, ‎is~the minimum cardinality of a total dominating set of G G ‎. ‎Chellali and Haynes [Total and paired-domination numbers of a tree, AKCE International ournal of Graphs and Combinatorics 1 (2004)‎, ‎69--75] established the following upper bound on the total domination number of a tree in terms of the order and the number of support vertices‎, ‎γ t (T)≤(n+s)/2 γt(T)≤(n+s)/2 ‎. ‎We characterize all trees attaining this upper bound‎.‎

‎Two types of properties for linear connections (natural and almost paracontact metric) are discussed in almost paracontact metric geometry with respect to four linear connections‎: ‎Levi-Civita‎, ‎canonical (Zamkovoy)‎, ‎Golab and generalized dual‎. ‎Their relationship is also analyzed with a special view towards their curvature‎. ‎The particular case of an almost paracosymplectic manifold gives a major simplification in computations since the paracontact form is closed‎.

The class of ads modules with the SIP (briefly‎, ‎SA SA -modules) is studied‎. ‎Various conditions for a module to be SA SA -module are given‎. ‎It is proved that for a quasi-continuous module M M ‎, ‎M M is a UC-module if and only if M M is an SA SA -module‎. ‎Also‎, ‎it is proved that the direct sum of two SA SA -modules as R R -modules is an SA SA -module when R R is the sum of the annihilators of these modules‎.

‎A ring R R is strongly clean provided that every element‎ ‎in R R is the sum of an idempotent and a unit that commutate‎. ‎Let‎ ‎T n (R,σ) Tn(R,σ) be the skew triangular matrix ring over a local‎ ‎ring R R where σ σ is an endomorphism of R R‎. ‎We show that‎ ‎T 2 (R,σ) T2(R,σ) is strongly clean if and only if for any a∈‎‎1+J(R)‎,‎b∈J(R) a∈‎‎1+J(R)‎,‎b∈J(R)‎, ‎l a −r σ(b) ‎:‎R→R la−rσ(b)‎:‎R→R is surjective‎. ‎Further‎, ‎T 3 (R,σ) T3(R,σ) is strongly clean if‎ ‎l a −r σ(b) ‎,‎l a −r σ 2 (b) la−rσ(b)‎,‎la−rσ2(b) and‎ ‎l b −r σ(a) lb−rσ(a) are surjective for any a∈U(R),b∈‎‎J(R) a∈U(R),b∈‎‎J(R) ‎. ‎The necessary condition for T 3 (R,σ) T3(R,σ) to be strongly‎ ‎clean is also obtained‎. ‎

‎In this paper‎, ‎we introduce α α -ψ ψ -contractive mapping in partially ordered sets and construct fixed point theorems to solve a first-order ordinary differential equation by existence of its lower solution.

Using the fixed point theorem in a‎ ‎cone‎, ‎the existence and multiplicity of radial convex solutions of‎ ‎singular system of Monge-Amp\`{e}re equations are established‎.‎

‎Making use of a linear operator‎, ‎which is defined here by means of‎ ‎the Hadamard product (or convolution)‎, ‎we define a subclass‎ ‎‎‎‎‎‎ Tp(a‎,‎c‎,‎γ‎,‎λ;h) of meromorphically‎ ‎multivalent functions‎. ‎The main object of this paper is to‎ ‎investigate some important properties for the class‎. ‎We also derive‎ ‎many results for the Hadamard roducts of functions belonging to the‎ ‎class.

‎In this paper‎, ‎we introduce and study a class of generalized vector quasi-equilibrium problem‎, ‎which includes many vector equilibrium problems‎, ‎equilibrium problems‎, ‎vector variational inequalities and variational inequalities as special cases‎. ‎Using one person game theorems‎, ‎the concept of escaping sequences and without convexity assumptions‎, ‎we prove some existence results for generalized vector quasi-equilibrium problem‎.

For a finite group G G ‎, ‎let Cent(G) Cent(G) denote the set of centralizers of single elements of G G ‎. ‎In this note we prove that if |G|≤32 |Cent(G)| |G|≤32|Cent(G)| and G G is 2-nilpotent‎, ‎then G≅S 3 ‎,‎D 10 G≅S3‎,‎D10 or S 3 ×S 3 S3×S3 ‎. ‎This result gives a partial and positive answer to a conjecture raised by A‎. ‎R‎. ‎Ashrafi [On finite groups with a given number of centralizers‎, ‎Algebra‎ ‎Colloq. 7 (2000)‎, ‎no‎. ‎2‎, ‎139- 146]‎.

In this paper, we investigate the existence of solution for a k-dimensional system of three points nabla fractional finite difference equations. Also, we present an example to illustrate our result.

In Proposition 2.6 in (G‎. ‎Gruenhage‎, ‎A‎. ‎Lutzer‎, ‎Baire and Volterra spaces‎, ‎\textit{Proc‎. ‎Amer‎. ‎Math‎. ‎Soc.} {128} (2000)‎, ‎no‎. ‎10‎, ‎3115--3124) a condition that‎ ‎every point of D D is G δ Gδ in X X was overlooked‎. ‎So we‎ ‎proved some conditions by which a Baire space is equivalent to a‎ ‎Volterra space‎. ‎In this note we show that if X X is a‎ ‎monotonically normal T 1 T1 -space with countable pseudocharacter ‎and X X has a σ σ -discrete dense subspace D D ‎, ‎then X X is a‎ ‎Baire space if and only if X X is Volterra‎. ‎We show that if X X ‎is a metacompact normal sequential T 1 T1 -space and X X has a‎ ‎σ σ -closed discrete dense subset‎, ‎then X X is a Baire space‎ ‎if and only if X X is Volterra‎. ‎If X X is a generalized ordered‎ ‎(GO) space and has a σ σ -closed discrete dense subset‎, ‎then‎ ‎X X is a Baire space if and only if X X is Volterra‎. ‎And also some‎ ‎known results are generalized‎.

‎In this paper a nonlinear backward parabolic problem in one‎ ‎dimensional space is considered‎. ‎Using a suitable iterative‎ ‎algorithm‎, ‎the problem is converted to a linear backward parabolic‎ ‎problem‎. ‎For the corresponding problem‎, ‎the backward finite‎ ‎differences method with suitable grid size is applied‎. ‎It is shown‎ ‎that if the coefficients satisfy some special conditions‎, ‎this‎ ‎algorithm not only is convergent‎, ‎but also is conditionally‎ ‎stable‎. ‎Moreover‎, ‎it is proved that the estimated values converge‎ ‎to the exact solution of the problem‎. ‎Al these‎ ‎approaches examined in some numerical examples. corresponding‎ ‎theorems for the convergency and stability of the solution are‎ ‎studied‎.

‎Let R R be a ring with involution ∗ ∗ ‎. ‎An additive mapping T:R→R T:R→R is called a left(respectively right) centralizer if T(xy)=T(x)y T(xy)=T(x)y (respectively T(xy)=xT(y) T(xy)=xT(y)) for all x,y∈R x,y∈R ‎. ‎The purpose of this paper is to examine the commutativity of prime rings with involution satisfying certain identities involving left centralizers.

‎By considering a degenerate p(x)− p(x)− Laplacian equation‎, ‎a generalized compact embedding in weighted variable‎ ‎exponent Sobolev space is presented‎. ‎Multiplicity of positive solutions are discussed by applying fibering map approach for the‎ ‎corresponding Nehari manifold‎.

For a finite group G G let nu(G) nu(G) denote the number of conjugacy classes of non-normal subgroups of G G. We give a short proof of a theorem of Brandl, which classifies finite groups with nu(G = nu(G)=1.

For Fracutemathbftexte acutemathbftexte chet algebras (A,(p n)) (A,(pn)) and (B,(q n)) (B,(qn)), a linear map T:ArightarrowB T:ArightarrowB is textit{almost multiplicative} with respect to (p n) (pn) and (q n) (qn), if there exists varepsilongeq0 varepsilongeq0 such that q n (Tab−TaTb)leqvarepsilonp n (a)p n (b), qn(Tab−TaTb)leqvarepsilonpn(a)pn(b), for all ninmathbbN ninmathbbN, a,binA a,binA, and it is called textit{weakly almost multiplicative} with respect to (p n) (pn) and (q n) (qn), if there exists varepsilongeq0 varepsilongeq0 such that for every kinmathbbN kinmathbbN, there exists n(k)inmathbbN n(k)inmathbbN, satisfying the inequality q k (Tab−TaTb)leqvarepsilonp n(k) (a)p n(k) (b), qk(Tab−TaTb)leqvarepsilonpn(k)(a)pn(k)(b), for all a,binA a,binA. We investigate the automatic continuity of (weakly) almost multiplicative maps between certain classes of Fracutemathbftexte acutemathbftexte chet algebras, such as Banach algebras and Fracutemathbftexte acutemathbftexte chet Q Q -algebras. We also obtain some results on the automatic continuity of dense range (weakly) almost multiplicative maps between Fracutemathbftexte acutemathbftexte chet algebras.

In this paper, we consider the boundedness of the Libera operator on Dirichlet spaces in terms of the Schur test. Moreover, we get its point spectrum and norm.

This paper deals with scrutinizing the convergence properties of iterative methods to solve linear system of equations. Recently, several types of the preconditioners have been applied for ameliorating the rate of convergence of the Accelerated Overrelaxation (AOR) method. In this paper, we study the applicability of a general class of the preconditioned iterative methods under certain conditions. More precisely, it is demonstrated that the preconditioned Mixed-Type Splitting (MTS) iterative methods can surpass the preconditioned AOR iterative methods for an entirely general class of preconditioners handled by Wang and Song [J. Comput. Appl. Math. 226 (2009), no. 1, 114--124]. Finally some numerical results are elaborated which confirm the validity of the established results.