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Variational inclusion governed by αβ-H((.,.),(.,.))-mixed accretive mapping

Gupta Sanjeev (Department of Economic Sciences Indian Institute of Technology Kanpur, Kanpur, India + Department of Mathematics, Shri Ram Murti Smarak College of Engineering and Technology, Bareilly, India)
Husain Shamshad (Department of Applied Mathematics, Aligarh Muslim University, Aligarh, India)
Mishra Vishnu Narayan (Department of Mathematics, Indira Gandhi National Tribal University, Lalpur, Amarkantak, India)

In this paper, we look into a new concept of accretive mappings called αβ-H((.,.),(.,.))-mixed accretive mappings in Banach spaces. We extend the concept of proximal-point mappings connected with generalized m-accretive mappings to the αβ-H((.,.),(.,.))-mixed accretive mappings and discuss its characteristics like single-valuable and Lipschitz continuity. Some illustration are given in support of αβ-H((.,.),(.,.))-mixed accretive mappings. Since proximal point mapping is a powerful tool for solving variational inclusion. Therefore, As an application of introduced mapping, we construct an iterative algorithm to solve variational inclusions and show its convergence with acceptable assumptions.

Keywords: αβ-H((.,.), (.,.))-mixed accretive mapping, proximal-point mapping, variational inclusion, iterative algorithm