Numerical Reckoning Fixed Points for Nonexpansive Mappings via a Faster Iteration Process and Its Application to Constrained Minimization Problems, Split Feasibility Problems and Image Deblurring Problems

Chonjaroen Chairatsiripong, Damrongsak Yambangwai, Tanakit Thianwan

Abstract


In this paper, we introduce a new faster iteration scheme and establish convergence results for approximation of fixed points of nonexpansive mappings in the framework of Banach space. Further, we show that our iteration process is faster than a number of existing iteration processes.  We support our analytic proof by  numerical examples in which we approximate the fixed point by a computer using Matlab program. Furthermore, we apply our results to find solutions of constrained minimization problems, split feasibility problems and image deblurring problems. Our results are the extension, improvement and generalizationof many known results in the literature of iterations in fixed point theory.

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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|