The Fixed Point Property in Banach Spaces with the NUS-Property

Abstract In this paper, we show that the weak nearly uniform smooth Banach spaces have the fixed point property for nonexpansive mappings.

On Strong Convergence of Halpern’s Method for Quasi-Nonexpansive Mappings in Hilbert Spaces

In this paper, we introduce a Halpern’s type method to approximate common fixed points of a nonexpansive mapping T and a strongly quasi-nonexpansive mappings S, defined in a Hilbert space, such that I − S is demiclosed at 0. The result shows as the same algorithm converges to different points, depending on the assumptions of the coefficients. Moreover, a numerical example of our iterative scheme is given.

Weak convergence theorems for asymptotically nonexpansive mappings and semigroups

Coincidence problems for generalized contractions

In this paper, we establish some new existence, uniqueness and Ulam-Hyers stability theorems for coincidence problems for two single-valued mappings. The main results of this paper extend the results presented in O. Mle?ni?e: Existence and Ulam-Hyers stability results for coincidence problems, J. Non-linear Sci. Appl., 6(2013), 108-116. In the last section two examples of application of these results are also given.

Property (M) and the weak fixed point property

It is shown that in Banach spaces with the property (M) of Kalton, nonexpansive self mappings of nonempty weakly compact convex sets necessarily have fixed points. The stability of this conclusion under renormings is examined and conditions for such spaces to have weak normal structure are considered.