Strong Convergence Theorem by Hybrid Method for Non-Lipschitzian Mapping

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...

Convergence Theorems For Two Finite Families of Uniformly L-Lipschitzian Mappings

Convergence theorems of hybrid methods for generalized mixed equilibrium problems and fixed point problems of an infinite family of Lipschitzian quasi-nonexpansive mappings in Hilbert spaces

We use a hybrid iterative method to find a common element of the set of fixed points of an infinite family of Lipschitzian quasi-nonexpansive mappings, the set of solutions of the general system of the variational inequality and the set of solutions of the generalized mixed equilibrium problem in real Hilbert spaces. We also show that our main strong convergence theorem for finding that common ...

Convergence theorem for an iterative algorithm of λ-strict pseudocontraction

In this article, we prove strong convergence of sequence generated by the following iteration sequence for a class of Lipschitzian pseudocontractive mapping T: x n+1 = β n u + (1 − β n)[α n Tx n + (1 − α n)x n ] whenever {a n } and {b n } satisfy the appropriate conditions.

Weak and Strong Convergence Theorems for Asymptotically Strict Pseudocontractive Mappings in the Intermediate Sense

We study the convergence of Ishikawa iteration process for the class of asymptotically κ-strict pseudocontractive mappings in the intermediate sense which is not necessarily Lipschitzian. Weak convergence theorem is established. We also obtain a strong convergence theorem by using hybrid projection for this iteration process. Our results improve and extend the corresponding results announced by...