General semi-implicit midpoint approximation for fixed point of almost contraction mapping and applications

Abstract

The objective of this paper is to suggest and construct a general four step semi-implicit iterative scheme involving midpoint rule. We establish and analyse the convergence of the suggested scheme to reckon the fixed point of an almost contraction mapping. Also, we prove the stability of the suggested iterative scheme. Finally, suggested method and our main results are applied to examine a general variational inequality and a nonlinear integral equation.

Keywords

• Convergence and stability
• general semi-implicit midpoint iteration
• fixed point
• almost contraction mapping
• general variational inequality
• integral equation