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Abstract <p> In this paper we introduce the notion of nonlinear search functionals in metric spaces and establish the existence of zeros for such functionals. We also present a theorem on the preservation of the existence of zeros of a one-parameter family of nonlinear search functionals. These results are then applied to derive some fixed point and coincidence point results for both single-valued and set-valued mappings. An illustrative example is provided to support our finding. </p>

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Zeros of Multi-Valued Functionals in Metric Spaces with Applications

  • 期刊论文

  • 发表日期：

    2025年10月1日

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  • L. V. Nguyen

摘要

Abstract

In this paper we introduce the notion of nonlinear search functionals in metric spaces and establish the existence of zeros for such functionals. We also present a theorem on the preservation of the existence of zeros of a one-parameter family of nonlinear search functionals. These results are then applied to derive some fixed point and coincidence point results for both single-valued and set-valued mappings. An illustrative example is provided to support our finding.