In this paper, we pursue two purposes. Our first goal is to study a new system of extended multi-valued nonlinear variational inclusions in Banach spaces and establish its equivalence with fixed point problems the help concept (H, ?)-proximal mapping. The obtained alternative equivalent formulation used iterative algorithm for finding approximate solution proposed. Under some appropriate assump...

In this paper we prove that the Newton method applied to the generalized equation y ∈ f(x) + F (x) with a C function f and a set-valued map F acting in Banach spaces, is locally convergent uniformly in the parameter y if and only if the map (f +F ) is Aubin continuous at the reference point. We also show that the Aubin continuity actually implies uniform Q-quadratic convergence provided that th...

In this article, we considered bidual spaces and reflexivity of real normed spaces. At first we proved some corollaries applying Hahn-Banach theorem and showed related theorems. In the second section, we proved the norm of dual spaces and defined the natural mapping, from real normed spaces to bidual spaces. We also proved some properties of this mapping. Next, we defined real normed space of R...

In this article, we considered bidual spaces and reflexivity of real normed spaces. At first we proved some corollaries applying Hahn-Banach theorem and showed related theorems. In the second section, we proved the norm of dual spaces and defined the natural mapping, from real normed spaces to bidual spaces. We also proved some properties of this mapping. Next, we defined real normed space of R...

The main result in this paper is the following linearization theorem. For each open set U in a complex Banach space E , there is a complex Banach space G°°(Í7) and a bounded holomorphic mapping gv: U —► G°°(U) with the following universal property: For each complex Banach space F and each bounded holomorphic mapping /: U —> F , there is a unique continuous linear operator T,\ G°°(U) —» F such t...

We give the weakest constraint qualification known to us that ensures the maximal monotonicity of the operator A∗ ◦ T ◦A when A is a linear continuous mapping between two reflexive Banach spaces and T is a maximal monotone operator. As a special case we get the weakest constraint qualification that ensures the maximal monotonicity of the sum of two maximal monotone operators on a reflexive Bana...

Let Z and X be Banach spaces, U ⊂ Z an open convex set and f : U → X a mapping. We say that f is a delta-convex mapping (d. c. mapping) if there exists a continuous convex function h on U such that y ◦ f + h is a continuous convex function for each y ∈ Y , ‖y∗‖ = 1. We say that f : U → X is locally d. c. if for each x ∈ U there exists an open convex U ′ such that x ∈ U ′ ⊂ U and f |U ′ is d. c....

in this paper we introduce new modified implicit and explicit algorithms and prove strong convergence of the two algorithms to a common fixed point of a family of uniformly asymptotically regularasymptotically nonexpansive mappings in a real reflexive banach space with a uniformly g$hat{a}$teaux differentiable norm. our result is applicable in $l_{p}(ell_{p})$ spaces,$1 < p

Let K be a subset of a real normed linear space E and let T be a self-mapping on K . T is said to be nonexpansive provided ‖Tx−Ty‖ ‖x− y‖ for all x, y ∈ K . Fixed-point iteration process for nonexpansive mappings in Banach spaces including Mann and Ishikawa iteration processes has been studied extensively by many authors to solve the nonlinear operator equations in Hilbert spaces and Banach spa...

The condition onto pair (F, G) of function Banach spaces under which there exists a integral operator T : F → G with analytic kernel such that the inverse mapping T −1 :imT → F does not belong to arbitrary a priori given Borel (or Baire) class is found. We begin with recalling some definitions [4, §31.IX]. Let X and Y be metric spaces. By definition, the family of analytically representable map...