Projection Type Ishikawa Iteration with Perturbations for Common Fixed Points of Two Nonself Generalized Asymptotically Quasi-Nonexpansive Mappings

Kritsadaphiwat Wongyai, Tanakit Thianwan

Abstract


In this paper, we introduce and study a new type of two-step iterative scheme which is called the projection type Ishikawa iteration with perturbations for two nonself generalized asymptotically quasi-nonexpansive mappings in Banach spaces. A sufficient condition for convergence of the iteration process to a common fixed point of mappings under our setting is also established in a real uniformly convex Banach space. Furthermore, the strong convergence of a new iterative scheme with perturbations to a common fixed point of two nonself generalized asymptotically quasi-nonexpansive mappings on a nonempty closed convex subset of a real Banach space is proved. The results obtained in this paper extend and generalize many important know results in recent literature.


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The Thai Journal of Mathematics organized and supported by The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART).

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|ISSN 1686-0209|