We study the class of separable (real) Banach spaces X which can be embedded into a space C(K) (K compact metric) in only one way up to automorphism. We show that in addition to the known spaces c0 (and all it subspaces) and 1 (and all its weak∗-closed subspaces) the space c0( 1) has this property. We show on the other hand (answering a question of Castillo and Moreno) that p for 1< p <∞ fails ...

Let X be a real reflexive Banach space and X∗ its dual space. Let T : X ⊃ D(T ) → 2X be an operator of class AG(S+), where G ⊂ X is open. An invariance of domain result for T will be discussed. This result extends a similar result of Park for single-valued operators of type (S+). The Skrypnik’s topological degree theory is used, utilizing approximating schemes of operators of class AG(S+), alon...

* Correspondence: [email protected]. th Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand Abstract In this article, we consider the solutions of the system of generalized variational inequality problems in Banach spaces. By employing the generalized projection operator, the well-known Fan’s KKM theorem and Kakutani-Fan-Glicksberg fixed point theorem, we...

In this paper, by using Bregman’s technique, we introduce and study the hybrid proximal-point methods for finding a common element of the set of solutions to a system of generalized equilibrium Problems and zeros of a finite family of maximal monotone operators in reflexive Banach spaces. Strong convergence results of the proposed hybrid proximal-point algorithms are also established under some...

Such a set G is said to be maximal monotone if it is maximal among monotone sets in the sense of set inclusion, and a mapping T is said to be maximal monotone if its graph G(T) is a maximal monotone set. For reflexive Banach spaces X and mappings T with D(T)~X, the basic result obtained independently by Browder [2] and Minty [20] states that if T is a monotone operator from D(T)=X to X* which i...

In this paper we construct a few iterative processes for computing {1, 2} inverses of a linear bounded operator, based on the hyper-power iterative method or the Neumann-type expansion. Under the suitable conditions these methods converge to the {1, 2, 3} or {1, 2, 4} inverses. Also, we specify conditions when the iterative processes converge to the Moore-Penrose inverse, the weighted Moore-Pen...

The purpose of this paper is to study a strong convergence of multi-step iterative scheme to a common solution for a finite family of strongly accretive operator equations in a reflexive Banach space with weakly continuous duality map. As a consequence, the strong convergence theorem for the multi-step iterative sequence to a common fixed point for finite family of strongly pseudocontractive ma...

In this paper, we present a few recent existence results via variational approach for the Cauchy problem dy dt (t) + A(t)y(t) ∋ f(t), y(0) = y0, t ∈ [0, T ], where A(t) : V → V ′ is a nonlinear maximal monotone operator of subgradient type in a dual pair (V, V ′) of reflexive Banach spaces. In this case, the above Cauchy problem reduces to a convex optimization problem via Brezis–Ekeland device...

In this paper, we investigate local properties in the system of completely 1-summing mapping spaces. We introduce notions injectivity, reflexivity, exactness, nuclearity and finite-representability First obtain that if V has WEP, is locally reflexive (Ⅱ1(⋅,⋅), π1(⋅)) only it (Ⅰ(⋅,⋅), t(⋅)). Furthermore prove an operator space ⊆ B(H) exact finitely representable {Mn}n∈N π1(⋅)). At last, show = C.

In this paper, we consider a class of non-autonomous nonlinear evolution equations in separable reflexive Banach spaces. First, linear problem and establish the approximate controllability results by finding feedback control with help an optimal problem. We then for semilinear differential equation spaces using theory systems, properties resolvent operator Schauder's fixed point theorem. Finall...