A proximal iterative algorithm for system of generalized nonlinear variational-like inequalities and fixed point problems

ABSTRACT

In this paper, we are concerned with the investigation problem of finding a common element of the set of fixed points of a total uniformly L-Lipschitzian mapping and the set of solutions of a system of generalized nonlinear variational-like inequalities. For this end, based on P-η-proximal mapping, an iterative algorithm is constructed and under some suitable conditions, the strong convergence and stability of the sequence generated by our proposed iterative algorithm to a common element of the above two sets are proved.

KEYWORDS:

• System of generalized nonlinear variational-like inequalities
• P–η-proximal mapping
• total uniformly L-Lipschitzian mapping

AMS MATHEMATICS SUBJECT CLASSIFICATIONS:

• 47H05
• 47H06
• 47H09
• 47J22

Disclosure statement

No potential conflict of interest was reported by the author(s).