Nonexpansive mappings and fixed-points in Banach spaces

Fixed Points of Non-Expansive Functions

“…Suppose t h a t / : (2 -+ E. We shall be interested in two conditions which may be satisfied by / : (1) or (2). / / the range off is bounded, then it has a fixed point.…”

“…We single out two results which can be deduced from Corollary 1.3. PROPOSITION (1) or (2), then it has a fixed point.…”

“…In this note we deal with fixed points of functions the range of which need not be contained in their domain of definition. Specifically, we discuss non-expansive mappings, defined on a convex subset of a Banach space, which satisfy condition (1). Our main result is Theorem 2.4.…”

Browder’s type convergence theorems for one-parameter semigroups of nonexpansive mappings in Banach spaces

“…We know that F (T ) is nonempty if C is weakly compact and has the fixed point property for nonexpansive mappings; see Bruck [9]. See also [3,6,14] and others. Browder's type convergence theorems for one-parameter semigroups of nonexpansive mappings are proved in [21][22][23][24][25] and others.…”

Asymptotically Non-Expansive Actions of Topological Semigroups and Fixed Points

“…DeMarr's theorem has been generalized in several directions by Belluce and Kirk in [1] and [2], W. Takahashi [9], T. Mitchell [8], and recently by the authors in [6] and [7].…”