Let H be a Hilbert space and let C be a closed convex nonempty subset of H and [Formula: see text] a non-self nonexpansive mapping. A map [Formula: see text] defined by [Formula: see text]. Then, for a fixed [Formula: see text] and for [Formula: see text], Krasnoselskii-Mann algorithm is defined by [Formula: see text] where [Formula: see text]. Recently, Colao and Marino (Fixed Point Theory App...

and Applied Analysis 3 Remark 1.1. If E is a reflexive strictly convex and smooth Banach space, then for x, y ∈ E, φ x, y 0 if and only if x y. It is sufficient to show that if φ x, y 0 then x y. From 1.6 , we have ‖x‖ ‖y‖. This implies 〈x, Jy〉 ‖x‖2 ‖Jy‖2. From the definitions of j, we have Jx Jy, that is, x y, see 8, 9 for more details. Let C be a nonempty closed convex subset of a smooth Bana...

* Correspondence: [email protected]. edu.tw Department of Mathematics, National Changhua University of Education, Changhua, 50058, Taiwan Full list of author information is available at the end of the article Abstract In this paper, we introduce generalized hybrid mapping on CAT(0) spaces. The class of generalized hybrid mappings contains the class of nonexpansive mappings, nonspreading mappings,...

Mean nonexpansive mappings were first introduced in 2007 by Goebel and Japón Pineda and advances have been made by several authors toward understanding their fixed point properties in various contexts. For any given mean nonexpansive mapping of a Banach space, many of the positive results have been derived from knowing that a certain average of some iterates of the mapping is nonexpansive. Howe...

There are two important connections between the classes of nonexpansive and of accretive mappings which give rise to a strong connection between the fixed point theory of nonexpansive mappings and the mapping theory of accretive maps. These are: (1) If U is a nonexpansive mapping of D(U) into X, and if we set T — I--U, D(T)=D(U), then T is an accretive mapping of D{T) into X. (2) If { U(i)f t^O...

In this paper, we investigate the existence of fixed points for Suzuki nonexpansive mappings in setting Banach spaces using asymptotic center technique. We also establish convergence regular approximate point sequence to mappings. Examples are given illustrate results. Our theorems generalize several results literature.

It is shown that any A-firmly, 0 < A < 1 , nonexpansive mapping T: C —> C has a fixed point in C whenever C is a finite union of nonempty, bounded, closed convex subsets of a uniformly convex Banach space. Let C be a nonempty subset of a Banach space X, and let X £ (0, 1). Then a mapping T: C —> X is said to be X-firmly nonexpansive if (1) \\Tx Ty\\ < ||(1 X)(x y)+X(Tx Ty)\\ for all x, y £ C. I...

‎inspired by the work of suzuki in‎ ‎[t. suzuki‎, ‎a generalized banach contraction principle that characterizes metric completeness‎, proc‎. ‎amer‎. ‎math‎. ‎soc. ‎136 (2008)‎, ‎1861--1869]‎, ‎we prove a fixed point theorem for contractive mappings‎ ‎that generalizes a theorem of geraghty in [m.a‎. ‎geraghty‎, ‎on contractive mappings‎, ‎proc‎. ‎amer‎. ‎math‎. ‎soc., ‎40 (1973)‎, ‎604--608]‎an...

and Applied Analysis 3 It is easy to see that a quasi-nonexpansive mapping is an asymptotically quasi-nonexpansive mapping with the sequence {1}. T is said to be asymptotically nonexpansive in the intermediate sense if and only if it is continuous, and the following inequality holds: lim sup n→∞ sup x,y∈C (∥ ∥Tx − Tny∥∥ − ∥∥x − y∥∥) ≤ 0. 2.6 T is said to be asymptotically quasi-nonexpansive in ...

the aim of this paper is to prove a common fixed point theorem for nonexpansive type single valued mappings which include both continuous and discontinuous mappings by relaxing the condition of continuity by weak reciprocally continuous mapping. our result is generalize and extends the corresponding result of jhade et al. [p.k. jhade, a.s. saluja and r. kushwah, coincidence and fixed points of ...