The notion of a bead metric space is defined as a nice generalization of the uniformly convex normed space such as $CAT(0)$ space, where the curvature is bounded from above by zero. In fact, the bead spaces themselves can be considered in particular as natural extensions of convex sets in uniformly convex spaces and normed bead spaces are identical with uniformly convex spaces. In this paper, w...

Let X be either a uniformly convex Banach space or a reflexive Banach space having the Opial property. It is shown that a multivalued nonexpansive mapping on a bounded closed convex subset of X has an endpoint if and only if it has the approximate endpoint property. This is the first result regarding the existence of endpoints for such kind of mappings even in Hilbert spaces. The related result...

We introduce composite implicit and explicit iterative algorithms for solving a general system of variational inequalities and a common fixed point problem of an infinite family of nonexpansive mappings in a real smooth and uniformly convex Banach space.These composite iterative algorithms are based on Korpelevich’s extragradient method and viscosity approximation method. We first consider and ...

The main result is that a separable Banach space with the weak∗ unconditional tree property is isomorphic to a subspace as well as a quotient of a Banach space with a shrinking unconditional basis. A consequence of this is that a Banach space is isomorphic to a subspace of a space with an unconditional basis iff it is isomorphic to a quotient of a space with an unconditional basis, which solves...

The notion of an asymptotic center is used to prove a number of results concerning the existence of fixed points under certain selfmappings of a closed and bounded convex subset of a uniformly convex Banach space.

Let E be a real q-uniformly smooth Banach space which is also uniformly convex and K be a nonempty, closed and convex subset of E. We obtain a weak convergence theorem of the explicit averaging cyclic algorithm for a finite family of asymptotically strictly pseudocontractive mappings of K under suitable control conditions, and elicit a necessary and sufficient condition that guarantees strong c...

and Applied Analysis 3 In this paper, we generalize and modify the iteration of Abbas et al. 7 from two mapping to the infinite family mappings {Ti : i ∈ N} of multivalued quasi-nonexpansive mapping in a uniformly convex Banach space. Let {Ti} be a countable family of multivalued quasi-nonexpansive mapping from a bounded and closed convex subset K of a Banach space into P K with F : ⋂∞ i 1 F Ti...

We introduce an iterative procedure for finding a point in the zero set (a solution to 0 ∈ A(v) and v ∈ C) of an inverse-monotone or inverse strongly-monotone operator A on a nonempty closed convex subset C in a uniformly smooth and uniformly convex Banach space. We establish weak convergence results under suitable assumptions.

‎The purpose of this paper is to introduce a new mapping for a finite‎ ‎family of accretive operators and introduce an iterative algorithm‎ ‎for finding a common zero of a finite family of accretive operators‎ ‎in a real reflexive strictly convex Banach space which has a‎ ‎uniformly G^ateaux differentiable norm and admits the duality‎ ‎mapping $j_{varphi}$‎, ‎where $varphi$ is a gauge function ...