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<p>The central theme of this article is the revision and expansion of Kannan and Reich type contractive conditions to accommodate couples and families of mappings. The purpose of these revision and expansion is to derive contractive conditions that can ensure the existence of common fixed points in complete spaces, even when compactness is not assumed. We execute our aim by utilizing two collections of real-valued control functions <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {S}\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal {U}\)</EquationSource> </InlineEquation> having certain properties and obtain some extended versions of Kannan and Reich type contractive conditions in such a way that the existence of common fixed point(s) of such extended mappings don’t require compactness of the underlying structure.</p>

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Revisiting common fixed points via Kannan and Reich type mappings

  • 期刊论文

  • 发表日期：

    2026年1月15日

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  • Hiranmoy Garai

摘要

The central theme of this article is the revision and expansion of Kannan and Reich type contractive conditions to accommodate couples and families of mappings. The purpose of these revision and expansion is to derive contractive conditions that can ensure the existence of common fixed points in complete spaces, even when compactness is not assumed. We execute our aim by utilizing two collections of real-valued control functions \(\mathcal {S}\) and \(\mathcal {U}\) having certain properties and obtain some extended versions of Kannan and Reich type contractive conditions in such a way that the existence of common fixed point(s) of such extended mappings don’t require compactness of the underlying structure.