DOI: 10.24193/fpt-ro.2025.1.19

Authors: S. Salisu, S. Sriwongsa, P. Kumam and V. Berinde

Abstract: This paper presents an adaptive algorithm for solving enriched contraction variational inequality problems, using the set of fixed points of an enriched nonexpansive mapping as a constrained set. The algorithm is defined within the framework of unique geodesic spaces. In each iteration, the scheme uses only two embedded geodesic segments and does not require the computation of any metric projection. The method requires one evaluation of an enriched nonexpansive mapping T₁ and an enriched contraction T₂ at every iteration. The convergence analysis of the proposed scheme is performed in the setting of CAT(0) spaces, and a numerical example is provided to support the findings.

Key Words and Phrases: Enriched contraction mapping, enriched nonexpansive mapping, fixed point, geodesic convexity, hierarchical variational inequality problem, viscosity scheme.

2010 Mathematics Subject Classification: 58E35, 47H05, 47H09, 47H10, 47J20.

Published on-line: February 1st, 2025.

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