Iterative Methods for Approximation of Fixed Points Via Like Contraction Mappings

Iterative methods for finding nearest common fixed points of a countable family of quasi-Lipschitzian mappings

We prove a strong convergence result for a sequence generated by Halpern's type iteration for approximating a common fixed point of a countable family of quasi-Lipschitzian mappings in a real Hilbert space. Consequently, we apply our results to the problem of finding a common fixed point of asymptotically nonexpansive mappings, an equilibrium problem, and a variational inequality problem for co...

Iterative Approximation of Fixed Points for Strongly Pseudo-contractive Mappings

The aim of this paper is to prove a convergence theorem of a generalized Ishikawa iteration sequence for two multivalued strongly pseudo-contractive mappings by using an approximation method in real uniformly smooth Banach spaces. We generalize and extend the results of Chang and Chang, Cho, Lee, Jung, and Kang.

Iterative approximation of fixed points of quasi-contraction mappings in cone metric spaces

*Correspondence: [email protected] Faculty of Mathematics and Informatics, University of Plovdiv, Plovdiv, 4000, Bulgaria Abstract In this paper, we establish a full statement of Ćirić’s fixed point theorem in the setting of cone metric spaces. More exactly, we obtain a priori and a posteriori error estimates for approximating fixed points of quasi-contractions in a cone metric space. Our ...

Iterative Methods for Approximation of Fixed Points and Their Applications

In this article, we deal with iterative methods for approximation of fixed points and their applications. We first discuss fixed point theorems for a nonexpansive mapping or a family of nonexpansive mappings. In particular, we state a fixed point theorem which answered affirmatively a problem posed during the Conference on Fixed Point Theory and Applications held at CIRM, Marseille-Luminy, 1989...

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points