Abstract:
One of our main results is the following convergencetheorem for one-parameter nonexpansive semigroups: let C be a bounded closed convex subset of a Hilbert space E, and let {T(t):t∈ℝ

Abstract:
We give one example for a one-parameter nonexpansive semigroup.This example shows that there exists a one-parameter nonexpansivesemigroup {T(t):t≥0} on a closed convex subset C of a Banach space E such that limt→∞‖(1/t)∫0tT(s)xds−x‖=0for some x∈C, which is not a common fixed point of {T(t):t≥0}.

Abstract:
Using the notion of Banach limits, we discuss the characterization of fixed points of nonexpansive mappings in Banach spaces. Indeed, we prove that the two sets of fixed points of a nonexpansive mapping and some mapping generated by a Banach limit coincide. In our discussion, we may not assume the strict convexity of the Banach space.

Abstract:
We prove that the recent fixed point theorem for contractions of integral type due to Branciari is a corollary of the famous Meir-Keeler fixed point theorem. We also prove that Meir-Keeler contractions of integral type are still Meir-Keeler contractions.

Abstract:
One of our main results is the following convergence theorem for one-parameter nonexpansive semigroups: let C be a bounded closed convex subset of a Hilbert space E , and let { T( t ):t∈ + } be a strongly continuous semigroup of nonexpansive mappings on C . Fix u∈C and t 1 , t 2 ∈ + with t 1 < t 2 . Define a sequence { x n } in C by x n = ( 1 α n ) / ( t 2 t 1 ) ∫ t 1 t 2 T( s ) x n ds+ α n u for n∈ , where { α n } is a sequence in ( 0,1 ) converging to 0 . Then { x n } converges strongly to a common fixed point of { T( t ):t∈ + } .

Abstract:
In this short paper, we prove fixed point theorems for nonexpansive mappings whose domains are unbounded subsets of Banach spaces. These theorems are generalizations of Penot's result in [4].

Abstract:
Using the notion of -distance, we prove several fixed point theorems, which are generalizations of fixed point theorems by Kannan, Meir-Keeler, Edelstein, and Nadler. We also discuss the properties of -distance.

Abstract:
If (X,d) is a complete metric space and T is a contraction on X, then the conclusion of the Banach-Caccioppoli contraction principle is that the sequence of successive approximations {Tnx} of T starting from any point x∈X converges to a unique fixed point. In this paper, using the concept of τ-distance, we obtain simple, sufficient, and necessary conditions of the above conclusion.

Abstract:
We prove Browder's type strong convergence theorems for infinite families of nonexpansive mappings. One of our main results is the following: let be a bounded closed convex subset of a uniformly smooth Banach space . Let be an infinite family of commuting nonexpansive mappings on . Let and be sequences in satisfying for . Fix and define a sequence in by for . Then converges strongly to , where is the unique sunny nonexpansive retraction from onto .

Abstract:
Using the notion of -distance, we prove several fixed point theorems, which are generalizations of fixed point theorems by Kannan, Meir-Keeler, Edelstein, and Nadler. We also discuss the properties of -distance.