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An Enhanced Subgradient Extragradient Method for Fixed Points of Quasi-Nonexpansive Mappings Without Demi-Closedness

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  • Anchalee Sripattanet

    (School of Education and Liberal Arts, Sarasas Suvarnabhumi Institute of Technology, Samut Prakan 10540, Thailand)

  • Atid Kangtunyakarn

    (Department of Mathematics, School of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand)

Abstract

This research focuses on developing a novel approach to finding fixed points of quasi-nonexpansive mappings without relying on the demi-closedness condition, a common requirement in previous studies. The approach is based on the Subgradient Extragradient technique, which builds upon the foundational extragradient method introduced by G.M. Korpelevich. Korpelevich’s method is a widely recognized tool in the fields of optimization and variational inequalities. This study extends Korpelevich’s technique by adapting it to a broader class of operators while maintaining critical convergence properties. This research demonstrates the effectiveness and practical applicability of this new method through detailed computational examples, highlighting its potential to address complex mathematical problems across various domains.

Suggested Citation

  • Anchalee Sripattanet & Atid Kangtunyakarn, 2025. "An Enhanced Subgradient Extragradient Method for Fixed Points of Quasi-Nonexpansive Mappings Without Demi-Closedness," Mathematics, MDPI, vol. 13(18), pages 1-28, September.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:18:p:2937-:d:1746835
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