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

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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.

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Acknowledgements

The authors would like to thank Naresuan University and King Mongkut’s University of Technology North Bangkok. We thank the anonymous referee for the careful reading of the paper and a valuable suggestion improving the presentation. This research was funded by King Mongkut’s University of Technology North Bangkok. Contract no. KMUTNB-63-DRIVE-16.

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Authors and Affiliations

  1. Faculty of Science Energy and Environment, King Mongkut’s University of Technology North Bangkok, Rayong Campus (KMUTNB), Rayong, 21120, Thailand

    Thidaporn Seangwattana

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

    Somyot Plubtieng

  3. Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok (KMUTNB), Wongsawang, Bangsue, Bangkok, 10800, Thailand

    Kanokwan Sitthithakerngkiet

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  1. Thidaporn Seangwattana
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Correspondence to Thidaporn Seangwattana.

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Communicated by T S S R K Rao, Phd.

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Seangwattana, T., Plubtieng, S. & Sitthithakerngkiet, K. A new linesearch iterative scheme for finding a common solution of split equilibrium and fixed point problems. Indian J Pure Appl Math 52, 614–628 (2021). https://doi.org/10.1007/s13226-021-00040-9

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