and Applied Analysis 3 Lemma 2.2 cf., 4 . Let D be a nonempty subset of a reflexive, strictly convex, and smooth Banach space E. Let R be a retraction from E onto D. Then R is sunny and generalized nonexpansive if and only if 〈 x − Rx, JRx − Jy ≥ 0, 2.2 for all x ∈ E and y ∈ D. A generalized resolvent Jr of a maximal monotone operator B ⊂ E∗ × E is defined by Jr I rBJ −1 for any real number r >...

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...

We introduce the classes of nearly contraction mappings and nearly asymptotically nonexpansive mappings. The class of nearly contraction mappings includes the class of contraction mappings, but the class of nearly asymptotically nonexpansive mappings contains the class of asymptotically nonexpansive mappings and is contained in the class of mappings of asymptotically nonexpansive type. We study...

for all x, y ∈ C and each n ≥ 1. The class of asymptotically nonexpansive mappings was introduced by Goebel and Kirk [1] as an important generalization of nonexpansive mappings. It was proved in [1] that if C is a nonempty bounded closed convex subset of a real uniformly convex Banach space and T is an asymptotically nonexpansive self mapping on C, then F (T ) is nonempty closed convex subset o...

for all x ∈ C, p ∈ F T and n ≥ 1. It is clear that if F T is nonempty, then the asymptotically nonexpansive mapping, the asymptotically quasi-nonexpansive mapping, and the generalized quasi-nonexpansive mapping are all the generalized asymptotically quasi-nonexpansive mapping. Recall also that a mapping T : C → C is said to be asymptotically quasi-nonexpasnive in the intermediate sense provided...

Recently, Chang, et al introduce the concept of total asymptotically nonexpansive mapping which contain the asymptotically nonexpansive mapping. The purpose of the paper is to analyze a three-step iterative scheme for total asymptotically nonexpansive mapping in uniformly convex hyperbolic spaces. Meanwhile, we obtain a ∆-convergence theorem of the three-step iterative scheme for total asymptot...

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.

In this paper we define g-nonexpansive and g-nonexpansive type fuzzy mappings and prove common fixed point theorems for sequences of fuzzy mappings satisfying certain conditions on a Banach space. Thus we obtain fixed point theorems for nonexpansive type multi-valued mappings.

We prove the demiclosedness principle for a class of mappings which is a generalization of all the forms of nonexpansive, asymptotically nonexpansive, and nearly asymptotically nonexpansive mappings. Moreover, we establish the existence theorem and convergence theorems for modified Ishikawa iterative process in the framework of CAT(0) spaces. Our results generalize, extend, and unify the corres...

and Applied Analysis 3 It is an interesting problem to extend the above results to a strongly continuous semigroup of nonexpansive mappings and a strongly continuous semigroup of asymptotically nonexpansive mappings. Let S be a strongly continuous semigroup of nonexpansive self-mappings. In 1998 Shioji and Takahashi 11 introduced, in Hilbert space, the implicit iteration