A Modified Mixed Ishikawa Iteration for Common Fixed Points of Two Asymptotically Quasi Pseudocontractive Type Non-Self-Mappings

A new modified mixed Ishikawa iterative sequence with error for common fixed points of two asymptotically quasi pseudocontractive type non-self-mappings is introduced. By the flexible use of the iterative scheme and a new lemma, some strong convergence theorems are proved under suitable conditions. The results in this paper improve and generalize some existing results.

Strong Convergence of a Modified Ishikawa Iterative Sequence for Asymptotically Quasi-Pseudo-Contractive-Type Mappings

The purpose of this paper is to investigate the strong convergence problem of a modified mixed Ishikawa iterative sequence with errors for approximating the fixed points of an asymptotically nonexpansive mapping in the intermediate sense and an asymptotically quasi-pseudo-contractive-type mapping in an arbitrary real Banach space. The results here improve and extend the corresponding results reported by some other authors recently.

Convergence theorems of a family of uniformly (L, α)-Lipschitz asymptotically quasi-nonexpansive type mappings

In this paper, we study the convergence of the Ishikawa iterative sequence of rank-

Approximation of fixed points of strongly pseudocontractive mappings in uniformly smooth Banach spaces

LetEbe a real uniformly smooth Banach space, andKa nonempty closed convex subset ofE. Assume thatT1+T2:K→Kis a continuous and strongly pseudocontractive mapping, whereT1:K→Kis Lipschitz andT2:K→Khas the bounded range mapping. Then the Ishikawa iterative sequence converges strongly to the unique fixed point ofT1+T2.

Iterative approximation of fixed point forΦ-hemicontractive mapping without Lipschitz assumption

LetEbe an arbitrary real Banach space and letKbe a nonempty closed convex subset ofEsuch thatK+K⊂K. Assume thatT:K→Kis a uniformly continuous andΦ-hemicontractive mapping. It is shown that the Ishikawa iterative sequence with errors converges strongly to the unique fixed point ofT.