Inertial Extragradient Method for Solving Variational Inequality and Fixed Point Problems of a Bregman Demigeneralized Mapping in a Reflexive Banach Spaces

Abstract

In this paper, by employing a Bregman distance approach, we introduce a self-adaptive inertial extragradient method for finding a common solution of variational inequality problem involving a pseudo-monotone operator and fixed point problem of a Bregman demigeneralized mapping in a reflexive Banach spaces. Using a Bregman distance approach, we establish a strong convergence result for approximating the common solution of the aforementioned problems under some mild assumptions. We display some numerical examples to show the performance of our iterative method. The result presented in this paper extends and complements many related results in literature.

Keywords:

• Bregman demigeneralized mapping
• fixed point problem
• iterative scheme
• pseudo-monotone operator
• variational inequality problem

2000 MATHEMATICS SUBJECT CLASSIFICATION::

• 47H06
• 47H09
• 47J05
• 47J25

Acknowledgement

The first author acknowledge with thanks the bursary and financial support from Department of Science and Technology and National Research Foundation, Republic of South Africa Center of Excellence in Mathematical and Statistical Sciences (DSI-NRF COE-MaSS) Post-Doctoral Bursary. Opinions expressed and conclusions arrived are those of the authors and are not necessarily to be attributed to the CoE-MaSS.