A New Iterative Algorithms for Finite Family of Resolvent Operators

Abstract

Depending on the needs and requirements of keeping up with the scientific procession, researchers tend to find new recurrence schemes or develop previous recurrence schemes that will help researchers reach the fixed point and solution of variational inequality. This article aims to provide novel approaches to finding a common fixed point of different types of important mappings and the set of zeros of maximal monotone operators. Also, we studied the weak and strong convergence of the proposed iterative method under some suitable conditions. To achieve this goal, we will introduce a new technical method of resolvent operators and metric projection using different types of function sequences, including sequence of maximal monotone operators, sequence of k-strictly pseudo-contractive mappings, and sequence of non-expansive mappings defined on nonempty convex- closed subset of Hilbert space.

Keywords

• Nonexpansive Mapping
• Metric Projection
• Strictly Pseudo Contraction Mapping
• Strongly Pseudo-Contractive
• Fixed Point