Korean J. Math. Vol. 27 No. 2 (2019) pp.297-327
DOI: https://doi.org/10.11568/kjm.2019.27.2.297

A new mapping for finding a common solution of split generalized equilibrium problem, variational inequality problem and fixed point problem

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Published: Jun 30, 2019
Keywords:
Split generalized equilibrium problem, Variational inequality problem, Fixed-point problem, Nonexpansive mapping
Mathematics Subject Classification:
49J30, 47H10, 47H17, 90C99

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Mohammad Farid
Unaizah College of Engineering Qassim University-51911, Kingdom of Saudi Arabia
Kaleem Raza Kazmi
Department of Mathematics Aligarh Muslim University Aligarh 202002, India

Abstract

In this paper, we introduce and study a general iterative algorithm to approximate a common solution of split generalized equilibrium problem, variational inequality problem and fixed point problem for a finite family of nonexpansive mappings in real Hilbert spaces. Further, we prove a strong convergence theorem for the sequences generated by the proposed iterative scheme. Finally, we derive some consequences from our main result. The results presented in this paper extended and unify many of the previously known results in this area.


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