Schauder bases and fixed points of nonexpansive mappings

Approximating fixed points of generalized nonexpansive mappings

Solutions of variational inequalities on fixed points of nonexpansive mappings

n this paper , we propose a generalized iterative method forfinding a common element of the set of fixed points of a singlenonexpannsive mapping and the set of solutions of two variationalinequalities with inverse strongly monotone mappings and strictlypseudo-contractive of Browder-Petryshyn type mapping. Our resultsimprove and extend the results announced by many others.

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...

Characterizations of fixed points of nonexpansive mappings

Let C be a closed convex subset of a Banach space E. A mapping T on C is called a nonexpansive mapping if ‖Tx−Ty‖ ≤ ‖x− y‖ for all x, y ∈ C. We denote by F(T) the set of fixed points of T . Kirk [17] proved that F(T) is nonempty in the case that C is weakly compact and has normal structure. See also [2, 3, 5, 6, 11] and others. Convergence theorems to fixed points are also proved by many author...

Nonexpansive mappings on complex C*-algebras and their fixed points

A normed space $mathfrak{X}$ is said to have the fixed point property, if for each nonexpansive mapping $T : E longrightarrow E $ on a nonempty bounded closed convex subset $ E $ of $ mathfrak{X} $ has a fixed point. In this paper, we first show that if $ X $ is a locally compact Hausdorff space then the following are equivalent: (i) $X$ is infinite set, (ii) $C_0(X)$ is infinite dimensional, (...