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...

Leptin decreases visceral fat (VF) and increases peripheral and hepatic insulin action. Here, we generated similar decreases in VF using leptin (Lep), β3-adrenoreceptor agonism (β3), or food restriction (FR) and asked whether insulin action would be equally improved. For 8 days before the in vivo study, Sprague-Dawley rats ( n = 24) were either fed ad libitum [control (Con)], treated with Lep o...

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.

*Correspondence: [email protected]; [email protected] Department of Mathematics, Tianjin Polytechnic University, Tianjin, 300387, China Abstract Let E be a uniformly convex and uniformly smooth Banach space, let C be a nonempty closed convex subset of E, let {Tn} : C→ C be a countable family of weak relatively nonexpansive mappings such that F = ⋂∞ n=1 F(Tn) = ∅. For any given gauss x0 ∈ C,...

In this paper, we study the properties of the metric projection operator (the nearest point projection operator) and its continuity. Then we use it to solve variational inequalities in general Banach spaces and to approximate the solutions in uniformly convex and uniformly smooth Banach spaces.

In this paper, a new iterative scheme by hybrid method is constructed. Strong convergence of the scheme to a common element of the set of fixed points of an infinite family of relatively quasi-nonexpansive mappings and set of common solutions to a system of equilibrium problems in a uniformly convex real Banach space which is also uniformly smooth is proved. Our results extend important recent ...

The purpose of this paper is to introduce and consider new hybrid proximal-type algorithms for finding a common element of the set EP of solutions of a generalized equilibrium problem, the set F S of fixed points of a relatively nonexpansive mapping S, and the set T−10 of zeros of a maximal monotone operator T in a uniformly smooth and uniformly convex Banach space. Strong convergence theorems ...