Bulletin of Iranian Mathematical Society
Volume:39 Issue: 3, 2013

In this paper, we prove the generalized Hyers-Ulam(or Hyers-Ulam-Rassias) stability of the following composite functional equation f(f(x)-f(y))=f(x+y)+f(x-y)-f(x)-f(y) in various normed spaces.

In this note we review a simple criterion, due to Ekedahl, for superspecial curves defined over finite fields.Using this we generalize and give some simple proofs for some well-known superspecial curves.

In the present paper, we give a necessary and sufficient condition for contact CR-warped product to be contact CR-product in Kenmotsu space forms.

begin{abstract} In this paper, we prove some strong and weak convergence of three step random iterative scheme with errors to common random fixed points of three asymptotically nonexpansive nonself random mappings in a real uniformly convex separable Banach space. end{abstract}

Let $G$ be a locally compact group, $H$ be a compact subgroup of $G$ and $varpi$ be a representation of the homogeneous space $G/H$ on a Hilbert space $mathcal H$. For $psi in L^p(G/H), 1leq p leqinfty$, and an admissible wavelet $zeta$ for $varpi$, we define the localization operator $L_{psi,zeta} $ on $mathcal H$ and we show that it is a bounded operator. Moreover, we prove that the localization operator is in Schatten $p$-class and also it is a compact operator for $ 1leq p leqinfty$.

In the present paper we introduce and study the notion of pairwise weakly Lindelof bitopological spaces and obtain some results. Further, we also study the pairwise weakly Lindelof subspaces and subsets, and investigate some of their properties. It was proved that a pairwise weakly Lindelof property is not a hereditary property.

Applications of hypergroups have mainly appeared in special subclasses. One of the importantsubclasses is the class of polygroups. In this paper, we study the notions of nilpotent and solvable polygroups by using the notion of heart of polygroups. In particular, we give a necessary and sufficient condition between nilpotent (solvable) polygroups and fundamental groups.

In this paper we show that if q is a power of a prime p, then the projective special linear group PSL(2, q) and the stabilizer of a point of the projective line have maximum sum element orders among all proper subgroups of projective general linear group PGL(2, q) for q odd and even respectively

In this paper we study the concept of ph-biatness of a Banach algebra A, where ph is a continuous homomorphism on A. We prove that if ph is a continuous epimorphism on A and A has a bounded approximate identity and A is ph- bi at, then A is ph-amenable. In the case where ph is an isomorphism on A we show that the ph- amenability of A implies its ph-bi atness.

For any group G, let C(G) denote the set of centralizers of G. We say that a group G has n centralizers (G is a Cn-group) if |C(G)| = n. In this note, we prove that every finite Cn-group with n ≤ 21 is soluble and this estimate is sharp. Moreover, we prove that every finite Cn-group with |G| < 30n+15 19 is non-nilpotent soluble. This result gives a partial answer to a conjecture raised by A. Ashrafi in 2000

A module $M$ is said to be coretractable if there exists a nonzero homomorphism of every nonzero factor of $M$ into $M$. We prove that all right (left) modules over a ring are coretractable if and only if the ring is Morita equivalent to a finite product of local right and left perfect rings.

‎We extend the method of adaptive two-stage sequential sampling to‎ ‎include designs where there is more than one criteria is used in‎ ‎deciding on the allocation of additional sampling effort‎. ‎These‎ ‎criteria‎, ‎or conditions‎, ‎can be a measure of the target‎ ‎population‎, ‎or a measure of some related population‎. ‎We develop‎ ‎Murthy estimator for the design that is unbiased estimators for‎ ‎the population mean‎, ‎and propose another‎, ‎more efficient‎, ‎estimator‎. ‎We investigate asymptotic properties of this estimator‎.‎We use a simulation study to investigate design properties of the‎ ‎multi-criteria adaptive sequential sampling scheme and also some‎ ‎estimator properties under the design‎.

Amonge other things we give sufficient and necessary conditions for the Lau product of Banachalgebras to be biflat or biprojective.

In this note we characterize polynomial numerical hulls of matrices $A in M_n$ such that $A^2$ is Hermitian. Also, we consider normal matrices $A in M_n$ whose $k^{th}$ power are semidefinite. For such matrices we show that $V^k(A)=sigma(A)$.

Let R be an associative ring with unity. An element a in R is said to be r-clean if a = e+r, where e is an idempotent and r is a regular (von Neumann) element in R. If every element of R is r-clean, then R is called an r-clean ring. In this paper, we prove that the concepts of clean ring and r-clean ring are equivalent for abelian rings. Further we prove that if 0 and 1 are the only idempotents in R, then an r-clean ring is an exchange ring. Also we show that the center of an r-clean ring is not necessary r-clean, but if 0 and 1 are the only idempotents in R, then the center of an r-clean ring is r-clean. Finally we give some properties and examples of r-clean rings