A new linesearch iterative scheme for finding a common solution of split equilibrium and fixed point problems

Thidaporn Seangwattana (), Somyot Plubtieng () and Kanokwan Sitthithakerngkiet ()
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Thidaporn Seangwattana: King Mongkut’s University of Technology North Bangkok
Somyot Plubtieng: Naresuan University
Kanokwan Sitthithakerngkiet: King Mongkut’s University of Technology North Bangkok (KMUTNB)

Indian Journal of Pure and Applied Mathematics, 2021, vol. 52, issue 2, 614-628

Abstract: Abstract In this paper, we propose a new linesearch iterative scheme for finding a common solution of split equilibrium and fixed point problems without pseudomonotonicity of the bifunction f in a real Hilbert space. When setting the solution of dual equilibrium problem is nonempty, we obtain a strong convergence theorem which is generated by the iterative scheme. Moreover, we also receive a new linesearch iterative scheme for finding a solution of the split equilibrium problem in suitable assumptions, and report some numerical results to illustrate the convergence of the proposed scheme.

Keywords: Fixed point problems; Hilbert spaces; Nonexpansive mappings; Split equilibrium problems; Strong convergence theorem (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13226-021-00040-9

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