Approximate Fixed Points for Nonexpansive and Quasi-Nonexpansive Mappings in Hyperspaces

Approximate Fixed Points for Nonexpansive and Quasi-Nonexpansive Mappings in Hyperspaces

Approximating Fixed Points of Nonexpansive Mappings in Hyperspaces

Let X be a nonempty compact subset of a Banach space (E,‖·‖), and let C(X) and CC(X) denote the families of all nonempty compact and all nonempty compact convex subsets of X , respectively. It is well known that (C(X),H) is compact, where H is the Hausdorff metric induced by ‖·‖. For A,B ∈ CC(X) and t ∈ R = (−∞,+∞), let A + B = {a + b : a∈ A, b ∈ B}, and let tA= {ta : a∈ A}. In the sequel, we a...

Common Fixed Points for Nonexpansive and Nonexpansive Type Fuzzy Mappings

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.

Approximating fixed points of generalized nonexpansive mappings

On fixed points of fundamentally nonexpansive mappings in Banach spaces

We first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a Banach space and next show that if the Banach space is having the Opial condition, then the fixed points set of such a mapping with the convex range is nonempty. In particular, we establish that if the Banach space is uniformly convex, and the range of such a mapping is bounded, closed and con...