Viscosity implicit midpoint scheme for enriched nonexpansive mappings

Abstract

This article proposes and analyses a viscosity scheme for an enriched nonexpansive mapping. The scheme is incorporated with the implicit midpoint rule of stiff differential equations. We deduce some convergence properties of the scheme and establish that a sequence generated therefrom converges strongly to a fixed point of an enriched nonexpansive mapping provided such a point exists. Furthermore, we provide some examples of the implementation of the schemes with respect to certain enriched mappings and show the numerical pattern of the scheme.

Keywords

• Enriched nonexpansive mapping
• implicit midpoint rule
• fixed point
• Hilbert space
• viscosity iteration

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