Common Fixed Points of Cq-Commuting Maps via Generalized Gregus-Type Inequalities

2025/06/18 by R., Babu G. V., Negash, Alemayehu, Bogale, Meaza
#47H10 #54H25 #FOS: Mathematics #General Mathematics (math.GM)

paper · doi:10.48550/arxiv.2507.02881

Abstract

We establish the existence of common fixed points for C_q-commuting self-mappings satisfying a generalized Gregus-type inequality with quadratic terms in q-starshaped subsets of normed linear spaces. Our framework extends classical fixed point theory through: (i) Set-distance constraints δ(⋅, [q, ⋅]) generalizing norm conditions (ii) Compatibility via C_q-commutativity without full affinity requirements (iii) Reciprocal continuity replacing full map continuity. Explicit examples (e.g., Example 2.6) demonstrate the non-triviality of these extensions. As applications, we derive invariant approximation theorems for best approximation sets. Our results generalize Nashine's work \citeNashine2007 and unify several known fixed point theorems.

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