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<p>This paper extends a recently introduced class of mappings contracting the total pairwise distances—an <i>n</i>-point extension of the Banach contraction principle—within the framework of semimetric spaces, employing triangle functions as defined by Bessenyei and Páles in [<CitationRef CitationID="CR13">13</CitationRef>]. We present new insights into fixed point theorems for this class, including its subclass of perimetric contractions on <i>k</i>-polygons, and demonstrate the applicability of these results beyond metric spaces to ultrametric spaces and distance spaces with power triangle functions.</p>

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MAPPINGS CONTRACTING THE TOTAL PAIRWISE DISTANCES IN SEMIMETRIC SPACES WITH TRIANGLE FUNCTIONS: PERIODIC AND MULTIPLE FIXED POINTS

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • Ravindra K. Bisht,
  • Evgen O. Petrov

摘要

This paper extends a recently introduced class of mappings contracting the total pairwise distances—an n-point extension of the Banach contraction principle—within the framework of semimetric spaces, employing triangle functions as defined by Bessenyei and Páles in [13]. We present new insights into fixed point theorems for this class, including its subclass of perimetric contractions on k-polygons, and demonstrate the applicability of these results beyond metric spaces to ultrametric spaces and distance spaces with power triangle functions.