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Existence theorems and iterative approximation methods for generalized mixed equilibrium problems for a countable family of nonexpansive mappings

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Abstract

In this paper, we introduce the new generalized mixed equilibrium problem basing on hemicontinuous and relaxed monotonic mapping. Using the KKM technique, we obtain the existence of solutions for the generalized mixed equilibrium problem in a Banach space. Furthermore, we also introduce a hybrid projection algorithm for finding a common element in the solution set of a generalized mixed equilibrium problem and the common fixed point set of a countable family of nonexpansive mappings. The strong convergence theorem of the proposed sequence is obtained in a Banach space setting. The main results extend various results existing in the current literature.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, 65000, Thailand

    Uthai Kamraksa & Rabian Wangkeeree

  2. Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok, 10400, Thailand

    Rabian Wangkeeree

Authors
  1. Uthai Kamraksa
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  2. Rabian Wangkeeree
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Correspondence to Rabian Wangkeeree.

Additional information

The project was supported by the “Centre of Excellence in Mathematics” under the Commission on Higher Education, Ministry of Education, Thailand and the grant from under the program Strategic Scholarships for Frontier Research Network for the Ph.D. Program Thai Doctoral degree from the Office of the Higher Education Commission.

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Kamraksa, U., Wangkeeree, R. Existence theorems and iterative approximation methods for generalized mixed equilibrium problems for a countable family of nonexpansive mappings. J Glob Optim 54, 27–46 (2012). https://doi.org/10.1007/s10898-011-9739-5

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  • DOI: https://doi.org/10.1007/s10898-011-9739-5

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