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<p>This paper introduces the notions of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(n\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>n</mi> </math></EquationSource> </InlineEquation>-tuple regularity and pseudo-Lipschitzness, providing a new regularity framework for families of set-valued mappings. These concepts enable the derivation of both exact and approximate results concerning the existence of cyclic fixed points. As special cases, we establish the existence of double fixed points and coincidence points in both complete and non-complete metric spaces. The assumptions adopted here are strictly weaker than those imposed in recent related works, and our results unify and extend several existing contributions in the literature.</p>

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n-tupled regularity and cyclic fixed points of multivalued mappings in metric spaces

  • 期刊论文

  • 发表日期：

    2026年4月20日

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  • Nguyen Huu Tron,
  • Michel Théra

摘要

This paper introduces the notions of \(n\) n -tuple regularity and pseudo-Lipschitzness, providing a new regularity framework for families of set-valued mappings. These concepts enable the derivation of both exact and approximate results concerning the existence of cyclic fixed points. As special cases, we establish the existence of double fixed points and coincidence points in both complete and non-complete metric spaces. The assumptions adopted here are strictly weaker than those imposed in recent related works, and our results unify and extend several existing contributions in the literature.