Sahand Communications in Mathematical Analysis
Volume:12 Issue: 1, Autumn 2018

Recently we generalized the max algebra system to the class of nonnegative tensors. In this paper we give some basic properties for the left (right) inverse, under the new system. The existence of order 2 left (right) inverse of tensors is characterized. Also we generalize the direct product of matrices to the direct product of tensors (of the same order, but may be different dimensions) and investigate its properties relevant to the spectral theory.

This paper aims at establishing the existence of results for a nonstandard equilibrium problems (EPN) . The solutions of this inequality are discussed in a subset K (either bounded or unbounded) of a Banach spaces X . Moreover, we enhance the main results by application of some differential inclusion.

In this paper a new class of sets called regular generalized δ -closed set (briefly rgδ -closed set)is introduced and its properties are studied. Several examples are provided to illustrate the behaviour of these new class of sets.

In this work, we study the existence of non-trivial multiple solutions for a class of quasilinear elliptic systems equipped with concave-convex nonlinearities and critical growth terms in bounded domains. By using the variational method, especially Nehari manifold and Palais-Smale condition, we prove the existence and multiplicity results of positive solutions.

Let (A,∥⋅∥) be a real Banach algebra, a complex algebra AC be a complexification of A and ∥|⋅∥| be an algebra norm on AC satisfying a simple condition together with the norm ∥⋅∥ on A. In this paper we first show that A∗ is a real Banach A∗∗-module if and only if (AC)∗ is a complex Banach (AC)∗∗-module. Next we prove that A∗∗ is (−1)-weakly amenable if and only if (AC)∗∗ is (−1)-weakly amenable. Finally, we give some examples of real Banach algebras which their second duals of some them are and of others are not (−1)-weakly amenable.

For a constant α∈(−π2,π2) , we define a subclass of the spirallike functions, SPp(α), the set of all functions f∈A \re{e−iαzf′(z)f(z)}≥∣∣∣zf′(z)f(z)−1∣∣∣. In the present paper, we shall give the estimate of the norm of the pre-Schwarzian derivative Tf=f′′/f′ where ∥Tf∥=supz∈Δ(1−|z|2)|Tf(z)| for the functions in SPp(α).

In this paper, first we use an example to show the efficiency of Miteration process introduced by Ullah and Arshad [4] for approximating fixed points of Suzuki generalized nonexpansive mappings. Then by using M iteration process, we prove some strong and Δ−convergence theorems for Suzuki generalized nonexpansive mappings in the setting of CAT(0) Spaces. Our results are the extension, improvement and generalization of many known results in CAT(0) spaces.

For two normed algebras A and B with the character space   △(B)≠∅  and a left B−module X,  a certain class of bounded linear maps from A into X is introduced. We set CMHB(A,X)  as the set of all non-zero B−character module homomorphisms from A into X. In the case where △(B)={φ} then CMHB(A,X)⋃{0} is a closed subspace of L(A,X)  of all bounded linear operators from A into X.   We  define an  equivalence  relation on  CMHB(A,X) and use it  to show that  CMHB(A,X)⋃{0} is  a union of closed subspaces of L(A,X).  Also some basic results and some hereditary properties are presented. Finally some relations between φ−amenable Banach algebras and character module homomorphisms are examined.

In this paper, we study Lp -conjecture on locally compact hypergroups and by some technical proofs we give some sufficient and necessary conditions for a weighted Lebesgue space Lp(K,w) to be a convolution Banach algebra, where 1<p<∞, K is a locally compact hypergroup and w is a weight function on K. Among the other things, we also show that if K is a locally compact hypergroup and p is greater than 2, K is compact if and only if m(K) is finite and f∗g exists for all f,g∈Lp(K), where m is a left Haar measure for K, and in particular, if K is discrete, K is finite if and only if the convolution of any two elements of Lp(K) exists.

The purpose of this paper is to introduce and study the concepts of fuzzy e-open set, fuzzy e-continuity and fuzzy e-compactness in intuitionistic fuzzy topological spaces. After giving the fundamental concepts of intuitionistic fuzzy sets and intuitionistic fuzzy topological spaces, we present intuitionistic fuzzy e-open sets and intuitionistic fuzzy e-continuity and other results related topological concepts. Several preservation properties and some characterizations concerning intuitionistic fuzzy e -compactness have been obtained.

This study after reviewing construction methods of generators in Archimedean copulas (AC), proposes several useful lemmas related with generators of AC. Then a new trigonometric Archimedean family will be shown which is based on cotangent function. The generated new family is able to model the low dependence structures.

This paper is devoted to the study of reproducing kernel Hilbert spaces. We focus on multipliers of reproducing kernel Banach and Hilbert spaces. In particular, we try to extend this concept and prove some related theorems. Moreover, we focus on reproducing kernels in vector-valued reproducing kernel Hilbert spaces. In particular, we extend reproducing kernels to relative reproducing kernels and prove some theorems in this subject.

In this paper, we study some growth properties of entire functions represented by a vector valued Dirichlet series on the basis of generalized relative Ritt order and generalized relative Ritt lower order.

Suppose that A is a semi-simple and commutative Banach algebra. In this paper we try to characterize the character space of the Banach algebra CBSE(Δ(A)) consisting of all BSE-functions on Δ(A) where Δ(A) denotes the character space of A. Indeed, in the case that A=C0(X) where X is a non-empty locally compact Hausdroff space, we give a complete characterization of Δ(CBSE(Δ(A))) and in the general case we give a partial answer. Also, using the Fourier algebra, we show that CBSE(Δ(A)) is not a C∗-algebra in general. Finally for some subsets E of A∗, we define the subspace of BSE-like functions on Δ(A)∪E and give a nice application of this space related to Goldstine's theorem.

In this paper, we propose a new approach to nonstandard analysis without using the ultrafilters. This method is very simple in practice. Moreover, we construct explicitly the total order relation in the new field of the infinitesimal numbers. To illustrate the importance of this work, we suggest comparing a few applications of this approach with the former methods.