A new hybrid projection algorithm is considered for a finite family of λi-strict pseudocontractions. Using the metric projection, some strong convergence theorems of common elements are obtained in a uniformly convex and 2-uniformly smooth Banach space. The results presented in this paper improve and extend the corresponding results of Matsushita and Takahshi, 2008, Kang and Wang, 2011, and man...

In this paper, we prove some strong and weak convergence theorems using a modified iterative process for nonself asymptotically nonexpansive mappings in a uniformly convex Banach space. This will improve and generalize the corresponding results in the existing literature. Finally, we will state that our theorems can be generalized to the case of finitely many mappings. c © 2007 Elsevier Ltd. Al...

Some algorithms for nding common xed point of a family of mappings isconstructed. Indeed, let C be a nonempty closed convex subset of a uniformlyconvex Banach space X whose norm is Gateaux dierentiable and let {Tn} bea family of self-mappings on C such that the set of all common fixed pointsof {Tn} is nonempty. We construct a sequence {xn} generated by the hybridmethod and also we give the cond...

Let $C$ be a nonempty closed convex subset of a real Banach space $E$, let $B: C rightarrow E $ be a nonlinear map, and let  $u, v$ be  positive numbers. In this paper, we show  that  the generalized variational inequality $V I (C, B)$ is singleton for $(u, v)$-cocoercive mappings under appropriate assumptions on Banach spaces. The main results are extensions of the Saeidi's Propositions for fi...

We study the asymptotic behavior of the sequence of the iterates for a nonexpansive mapping, defined on a suitable subset of a Banach space with Opial's condition. Some results are stated also for semigroups of nonexpansive mappings and for mappings of asymptotically nonexpansive type in uniformly convex Banach spaces with Opial's condition.

We prove that for κ an uncountable cardinal, there exist 2κ many non homeomorphic weakly compact convex subsets of weight κ in the Hilbert space l2(κ).

In this paper, we introduce operator s-convex functions and establish some Hermite-Hadamard type inequalities in which some operator s-convex functions of positive operators in Hilbert spaces are involved.

We consider the minimization of convex functionals on a real Hilbert space. The requisite theory is reviewed, and concise proofs of the relevant results are given.

• Positivity: N(v) ≥ 0 with equality if and only if v = 0. • Positive Homogeneity: N(αv) = |α|N(v). • Triangle Inequality: N(x1 + x2) ≤ N(x1) +N(x2). If N is a norm for V then we call ρ N (x1, x2) := N(x1−x2) the associated distance function (or metric) for V . A vector space V together with some a choice of norm is called a normed space, and the norm is usually denoted by ‖ ‖. If V is complete...

The Hilbert geometry in an open bounded convex set in R is a classical example of a projective Finsler space. We construct explicitly a positive measure on the space of lines in a polytopal Hilbert geometry which yields an integral geometric representation of Crofton type for the Holmes-Thompson area of hypersurfaces. MSC 2000: 53C60 (primary); 53C65, 52B11 (secondary)