Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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APPROXIMATION METHODS FOR SOLVING SPLIT EQUALITY OF VARIATIONAL INEQUALITY AND f, g-FIXED POINT PROBLEMS IN REFLEXIVE BANACH SPACES

  • Yirga Abebe Belay (Department of Mathematics and Statistical Sciences, Faculty of Sciences, Botswana International University of Science and Technology) ;
  • Habtu Zegeye (Department of Mathematics and Statistical Sciences, Faculty of Sciences, Botswana International University of Science and Technology) ;
  • Oganeditse A. Boikanyo (Department of Mathematics and Statistical Sciences, Faculty of Sciences, Botswana International University of Science and Technology)
  • Received : 2022.03.15
  • Accepted : 2022.10.12
  • Published : 2023.03.03
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Abstract

The purpose of this paper is to introduce and study a method for solving the split equality of variational inequality and f, g-fixed point problems in reflexive real Banach spaces, where the variational inequality problems are for uniformly continuous pseudomonotone mappings and the fixed point problems are for Bregman relatively f, g-nonexpansive mappings. A strong convergence theorem is proved under some mild conditions. Finally, a numerical example is provided to demonstrate the effectiveness of the algorithm.

Keywords

Acknowledgement

The first and the second authors would like to gratefully acknowledge the funding received from Simons Foundation based at Botswana International University of Science and Technology (BIUST).

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