The Theory of the Feasibility Problems and Fixed Point Problems of Nonlinear Mappings

Sirawit Premjitpraphan, Atid Kangtunyakarn

Abstract


In this paper, we extended and improve some results of Hamdi [ Hamdi, A., Liou, Y.C., Yao, Y. and Luo, C.: The common solutions of the split feasibility problems and fixed point problems. Journal of Inequalities and Applications (2015) 2015:385 DOI10.1186/s13660-015-0870-6] by using the concept of lemma 2.11 Suwannaut and Kangtunyakarn [Suwannaut, S. and Kangtunyakarn, A.: The combination of the set of solutions of equilibrium problem for convergence theorem of the set of fixed points of strictly pseudo-contractive mappings and variational inequalities problem. Fixed Point Theory and its Applications (2013) 2013:291]. Then we prove strong convergence theorem of the proposed iteration under some control condition. Moreover, we use S-mapping in application with our main result.

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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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