Many optimization problems can be reformulated as best approximation problems with respect to an appropriate norm. Their solutions are thus given by projection operators. It follows that projection operators play a key role in several areas, such as mechanics, minimization algorithms, variational inequalities, complementary problems. Thus, it is of interest to study the properties of such opera...

Throughout this paper, we assume that X is a uniformly convex Banach space and X∗ is the dual space of X. Let J denote the normalized duality mapping form X into 2 ∗ given by J x {f ∈ X∗ : 〈x, f〉 ‖x‖2 ‖f‖2} for all x ∈ X, where 〈·, ·〉 denotes the generalized duality pairing. It is well known that if X is uniformly smooth, then J is single valued and is norm to norm uniformly continuous on any b...

The purpose of this paper is to propose a compositeiterative scheme for approximating a common solution for a finitefamily of m-accretive operators in a strictly convex Banach spacehaving a uniformly Gateaux differentiable norm. As a consequence,the strong convergence of the scheme for a common fixed point ofa finite family of pseudocontractive mappings is also obtained.

This paper discusses under what conditions two disjoint convex subsets of a linear topological space can be separated by a continuous linear functional. The equivalence of several forms of the Hahn-Banach theorem is proven. The separation problem is considered in linear topological spaces, locally convex linear topological spaces, Banach spaces, and finally finite dimensional Banach spaces. A n...

Maximal monotone operators on a Banach space into its dual can be represented by convex functions bounded below by the duality product. It is natural to ask under which conditions a convex function represents a maximal monotone operator. A satisfactory answer, in the context of reflexive Banach spaces, has been obtained some years ago. Recently, a partial result on non-reflexive Banach spaces w...

in this paper, we obtained the convergence of modified noor iterative scheme for nearly lipschitzian maps in real banach spaces. our results contribute to the literature in this area of re- search.

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}

In this paper, we introduce and study an inertial algorithm for approximating solutions of split equality fixed point problem (SEFPP), involving quasi-phi-nonexpansive mappings in uniformly smooth 2-uniformly convex real Banach spaces establish a strong convergence theorem. We give applications our result to (SEP), variational inclusion (SEVIP) equilibrium (SEEP). Our results extend, generalize...

Abstract In this paper, we introduce an inertial Halpern-type iterative algorithm for approximating a zero of the sum two monotone operators in setting real Banach spaces that are 2-uniformly convex and uniformly smooth. Strong convergence sequence generated by our proposed is established means some new geometric inequalities proved paper independent interest. Furthermore, numerical simulations...