nonexpansive mappings on complex $mathsf{c}^star$--algebras and their fixed points

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, (...

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.

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...

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.

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...