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<p>In this article, we present a hybrid algorithm designed to find the global minimum of the best proximity points for a proximal <i>b</i>-enriched nonexpansive mapping, named as enriched best proximity point. We also provide proof of strong convergence for our proposed method, under appropriate conditions in real Hilbert spaces. To demonstrate effectively enriched nonexpansiveness of our approach, we include numerical examples. Furthermore, we apply our results to solve a split feasibility problem in Hilbert spaces.</p>

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Enriched best proximity point theorems for enriched non-self nonexpansive mappings with an application in Hilbert spaces

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月19日

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  • Saima Kanwal,
  • Naeem Saleem,
  • Mi Zhou,
  • Asima Razzaque

摘要

In this article, we present a hybrid algorithm designed to find the global minimum of the best proximity points for a proximal b-enriched nonexpansive mapping, named as enriched best proximity point. We also provide proof of strong convergence for our proposed method, under appropriate conditions in real Hilbert spaces. To demonstrate effectively enriched nonexpansiveness of our approach, we include numerical examples. Furthermore, we apply our results to solve a split feasibility problem in Hilbert spaces.