Search

Let A be a Banach algebra. An element a ϵ A has generalized Drazin inverse if there exists b ϵ A such that b = bab, ab = ba, a - a²b ϵ Aqnil. New additive results for the generalized Drazin inverse of an operator over a Banach space are presented. we extend the main results of a paper of Shakoor, Yang and Ali from 2013 and of Wang, Huang and Chen from 2017. Appling these results to 2 x 2 operator matrices we also generalize results of a paper of Deng, Cvetković-Ilić and Wei from 2010. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an inertial self-adaptive projection method using Bregman distance techniques for solving pseudomonotone equilibrium problems in reflexive Banach spaces. The algorithm requires only one projection onto the feasible set without any Lipschitz-like condition on the bifunction. Using this method, a strong convergence theorem is proved under some mild conditions. Furthermore, we include numerical experiments to illustrate the behaviour of the new algorithm with respect to the Bregman function and other algorithms in the literature. [ABSTRACT FROM AUTHOR]

In this paper, starting with the geometric constants that can characterize Hilbert spaces, combined with the isosceles orthogonality of Banach spaces, the orthogonal geometric constant ΩX(α) is defined, and some theorems on the geometric properties of Banach spaces are derived. Firstly, this paper reviews the research progress of orthogonal geometric constants in recent years. Then, this paper explores the basic properties of the new geometric constants and their relationship with conventional geometric constants, and deduces the identity of ΩX(α) and X(α). Finally, according to the identities, the relationship between these the new orthogonal geometric constant and the geometric properties of Banach Spaces (such as uniformly non-squareness, smoothness, convexity, normal structure, etc.) is studied, and some necessary and sufficient conditions are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we study some fixed point properties of n-generalized Bregman nonspreading mappings in reflexive Banach space. We introduce a hybrid iterative scheme for finding a common solution for a countable family of equilibrium problems and fixed point problems in reflexive Banach space. Further, we give some applications and numerical example to show the importance and demonstrate the performance of our algorithm. The results in this paper extend and generalize many related results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce two new geometric constants related to the heights of triangles: - Δ(X) and - Δ(X, I). We also propose two new geometric constants, - Δ(X) and - Δ(X), related to the midlines of equilateral triangles, and discuss the relation between the heights and midlines in equilateral triangles. We give estimates for these geometric constants in terms of other geometric parameters, and the geometric constants are used to discuss geometric properties such as uniform non-squareness, uniform normal structure, and the fixed point property. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new iterative algorithm generated by a finite family of accretive operators in a q-uniformly smooth Banach space. We prove the strong convergence of the proposed iterative algorithm. The results presented in this paper are interesting extensions and improvements of known results of Qin et al. [Fixed Point Theory Appl. 2014(2014): 166], Kim and Xu [Nonlinear Anal. 61(2005), 51–60] and Benavides et al. [Math. Nachr. 248(2003), 62–71]. [ABSTRACT FROM AUTHOR]

In this paper, we present and prove new existence and uniqueness fixed point theorems for vector operators having a mixed monotone property in partially ordered product Banach spaces. Our results extend and improve existing works on T-φ-concave operators in the scalar case. As an application, we study the existence and uniqueness of positive solutions for systems of nonlinear Neumann boundary value problems. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study a new system of variational inclusions with B-monotone operators in Banach spaces. By using the proximal mapping associated with B- monotone operator, we construct a new iterative algorithm for approximating the solution of this system of variational inclusions. We also prove the existence of solutions and the convergence of the sequences generated by the algorithm for this system of variational inclusions. The results presented in this paper extend and improve some known results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we consider a system of nonlinear variational type inclusions involving (H, η, φ)-monotone operators in real Banach spaces. Further, we define a proximal operator associated with an (H; η; φ)-monotone operator and show that it is single valued and Lipschitz continuous. Using proximal point operator techniques, we prove the existence and uniqueness of a solution and suggest an iterative algorithm for the system of nonlinear variational type inclusions. Furthermore, we discuss the convergence of the iterative sequences generated by the algorithms. [ABSTRACT FROM AUTHOR]

In this paper, a new one-step iterative scheme with error for approximating common fixed points of asymptotically quasi-nonexpansive type nonself-mappings in Banach space is defined. The results obtained in this paper extend and improve the recent ones, announced by H. Y. Zhou, Y. J. Cho, and S. M. Kang [Zhou et al.,(2007), namely, A new iterative algorithm for approximating common fixed points for asymptotically non- expansive mappings, published to Fixed Point Theory and Applications 2007 : 1-9], and many others. [ABSTRACT FROM AUTHOR]

G-vector-valued sequence space frames and g-Banach frames for Banach spaces are introduced and studied in this paper. Also, the concepts of duality mapping and β-dual of a BK-space are used to define frame mapping and synthesis operator of these frames, respectively. Finally, some results regarding the existence of g-vector-valued sequence space frames and g-Banach frames are obtained. In particular, it is proved that if X is a separable Banach space and Y is a Banach space with a Schauder basis, then there exist a Y -valued sequence space Yv and a g-Banach frame for X with respect to Y and Yv. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of convergence of an iterative algorithm for a general system of variational inequalities, a nonexpansive mapping and an η-strictly pseudo-contractive mapping. Strong convergence theorems are established in the framework of real Banach spaces. [ABSTRACT FROM AUTHOR]

The aim of this paper is to prove strong convergence theorem by a modified three step iterative process with errors for three nonexpansive mappings in the frame work of uniformly smooth Banach spaces. The main feature of this scheme is that its special cases can handle both strong convergence like Halpern type and weak convergence like Ishikawa type iteration schemes. Our result extend and generalize the result of S. H. Khan [10], Kim and Xu [12] and many other authors. [ABSTRACT FROM AUTHOR]

In this paper, we prove the generalized Hyers-Ulam stability of the following Jensen type functional equation f(x-y/n + z) + f(y-z/n + x) + f(z-x/n + y) = f(x) + f(y) + f(z) in p-Banach spaces for any fixed nonzero integer n. [ABSTRACT FROM AUTHOR]

Let A be a Banach ternary algebra over a scalar field R or C and X be a ternary Banach A-module. A quartic mapping D : (A, []A) → (X, []x) is called a 4th-order ternary derivation if D([x, y, z]) = [D(x), y4, z4 + [x4 D(y), z4 + [x4, y4, D(z)] for all x, y, z ∈ A. In this paper, we prove Ulam stability generalizations of 4th - order ternary derivations associated to the following JMRassias quartic functional equation on fréchet algebras: f(kx + y) + f(kx - y) = k²[f(x + y) + f(x - y)] + 2k²(k - 1)f(x) - 2(k² - 1)f(y). [ABSTRACT FROM AUTHOR]

In this paper, we first introduce a family S = {Sn : C → C} of non-Lipschitzian mappings, called total asymptotically nonexpansive (briefly, TAN) on a nonempty closed convex subset C of a real Banach space X, and next give necessary and sufficient conditions for strong convergence of the sequence fxng defined recursively by the algorithm xn+1 = Snxn; n ≥ 1, starting from an initial guess x1 ϵ C, to a common fixed point for such a continuous TAN family S in Banach spaces. Finally, some applications to a finite family of TAN self mappings are also added. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the Hyers-Ulam-Rassias stability of a bi-Jensen functional equation 4f(These equations cannot be represented into ASCII text) = f(x, z) + f(x,w) + f(y, z) + f(y,w). [ABSTRACT FROM AUTHOR]

In this paper we study the existence of global small solutions of the Cauchy problem for the non-isotropically perturbed nonlinear Schrödinger equation: iut + Δu + ∣u∣α u + a Σid uxixixixi = 0, where a is real constant, 1 ≤ d < n is a integer, α is a positive constant, and x = (x1, x2, … , xn) ∈ Rn. For some admissible α we show the existence of global(almost global) solutions and we calculate the regularity of those solutions. [ABSTRACT FROM AUTHOR]

We investigate the generalized Hyers-Ulam-Rassias stability in p-Banach spaces for the following functional equation which is two types, that is, either cubic or quadratic: 2f(x + 3y) + 6f(x - y) + 12f(2y) = 2f(x - 3y) + 6f(x + y) + 3f(4y). The concept of Hyers-Ulam-Rassias stability originated essentially with the Th. M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297-300. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence of solutions of second order impulsive neutral functional differential inclusions which the nonlinearity F admits convex and non-convex values. Some results under weaker conditions are presented. Our results extend previous ones. The methods rely on a fixed point theorem for condensing multivalued maps and Schaefer's fixed point theorem combined with lower semi-continuous multivalued operators with decomposable values. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study a new class containing absolutely summing multilinear mappings and polynomials, which we call multiple weakly summing multilinear mappings and polynomials. We investigate some interesting properties about multiple weakly (p; q1, ⋯ , qκ)-summing multilinear mappings and polynomials defined on Banach spaces: In particular, we prove a kind of Dvoretzky-Rogers' Theorem and an ideal property for multiple weakly (p; q1, ⋯ , qκ)-summing multilinear mappings and polynomials. We also prove that the Aron-Berner extensions of multiple weakly (p; q1, ⋯ , qκ)- summing multilinear mappings and polynomials are also multiple weakly (p; q1, ⋯ , qκ)- summing. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of a system of asymptotically quasi-nonexpansive type mappings. Furthermore, we define a k-step iterative sequence approximating common fixed point for a system of asymptotically quasi-nonexpansive type mappings and study its stability in real Banach spaces. [ABSTRACT FROM AUTHOR]

In this paper, we first define a new kind of two-weight-Arλ3 (λ1, λ2, Ω)-weight, and then prove the imbedding inequalities for A-harmonic tensors. These results can be used to study the weighted norms of the homotopy operator T from the Banach space Lp(D,Λl) to the Sobolev space W1,p(D,Λl-1), l = 1, 2, …, n, and to establish the basic weighted Lp-estimates for A-harmonic tensors. [ABSTRACT FROM AUTHOR]

Let f denote a mapping from an orthogonality space (X,⊥) into a real Banach space Y. In this paper, we prove the Hyers-Ulam-Rassias stability of the orthogonally cubic functional equations f(2x + y) + f(2x - y) = 2f(x + y) + 2f(x - y) + 12f(x) and f(x + y + 2z) + f(x + y - 2z) + f(2x) + f(2y) = 2f(x + y)+ 4f(x + z)+ 4f (x - z) + 4f(y + z) + 4f(y - z), where x ⊥ y, y ⊥ z, x ⊥ z. [ABSTRACT FROM AUTHOR]

Suppose C is a nonempty closed convex subset of a real uniformly convex Banach space X. Let T : C → C be an asymptotically nonexpansive in the intermediate sense mapping. In this paper we introduced the three-step iterative sequence for such map with error members. Moreover, we prove that, if T is completely continuous then the our iterative sequence converges strongly to a fixed point of T. [ABSTRACT FROM AUTHOR]

In this paper, we have shown that the convergence of one-step, two-step and three-step iterations is equivalent, which are known as Mann, Ishikawa and Noor iteration procedures, for a special class of Lipschitzian operators defined in a closed, convex subset of an arbitrary Banach space. [ABSTRACT FROM AUTHOR]

In this paper, we have shown that the convergence of one-step, two-step and three-step iterations is equivalent, which are known as Mann, Ishikawa and Noor iteration procedures, for a special class of Lipschitzian operators defined in a closed, convex subset of an arbitrary Banach space. [ABSTRACT FROM AUTHOR]

Suppose C is a nonempty closed convex subset of a real uniformly convex Banach space X. Let T : C → C be an asymptotically nonexpansive in the intermediate sense mapping. In this paper we introduced the three-step iterative sequence for such map with error members. Moreover, we prove that, if T is completely continuous then the our iterative sequence converges strongly to a fixed point of T. [ABSTRACT FROM AUTHOR]