We introduce some condition on mappings. The condition is weaker than nonexpansiveness and stronger than quasinonexpansiveness. We present fixed point theorems and convergence theorems for mappings satisfying the condition.
Abstract. We prove a fixed point theorem that is a very simple generalization of the Banach contraction principle and characterizes the metric completeness of the underlying space. We also discuss the Meir-Keeler fixed point theorem.
In this paper we introduce two new classes of generalized nonexpansive mapping and we study both the existence of fixed points and their asymptotic behavior.
The c-erbB-2 gene is a v-erbB-related proto-oncogene which is distinct from the gene encoding the epidermal growth factor receptor. By using two independent methods, hybridization of both sorted chromosomes and metaphase spreads with cloned c-erbB-2 DNA, we mapped the c-erbB-2 locus on human chromosome 17 at q21, a specific breakpoint observed in a translocation associated with acute promyelocytic leukemia. Furthermore, we observed amplification and elevated expression of the c-erbB-2 gene in the MKN-7 gastric cancer cell line. These data suggest possible involvement of the c-erbB-2 gene in human cancer.
In this paper, we prove Krasnoselskii and Mann's type convergence theorems for nonexpansive semigroups without using Bochner integral and without assuming the strict convexity of Banach spaces. One of our main results is the following: let C be a compact convex subset of a Banach space E and let {T (t): t 0} be a one-parameter strongly continuous semigroup of nonexpansive mappings on C. Let {t n } be a sequence in [0, ∞) satisfying lim inf n→∞ t n < lim sup n→∞ t n and lim n→∞ (t n+1 − t n ) = 0.Let λ ∈ (0, 1). Define a sequence {x n } in C by x 1 ∈ C and x n+1 = λT (t n )x n + (1 − λ)x n for n ∈ N. Then {x n } converges strongly to a common fixed point of {T (t): t 0}. 2004 Elsevier Inc. All rights reserved.
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