Common Fixed Points of Cq-Commuting Maps via Generalized Gregus-Type Inequalities
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908433428512768 |
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| author | R., Babu G. V. Negash, Alemayehu Bogale, Meaza |
| author_facet | R., Babu G. V. Negash, Alemayehu Bogale, Meaza |
| contents | 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 $δ(\cdot, [q, \cdot])$ 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 \cite{Nashine2007} and unify several known fixed point theorems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_02881 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Common Fixed Points of Cq-Commuting Maps via Generalized Gregus-Type Inequalities R., Babu G. V. Negash, Alemayehu Bogale, Meaza General Mathematics 47H10, 54H25 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 $δ(\cdot, [q, \cdot])$ 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 \cite{Nashine2007} and unify several known fixed point theorems. |
| title | Common Fixed Points of Cq-Commuting Maps via Generalized Gregus-Type Inequalities |
| topic | General Mathematics 47H10, 54H25 |
| url | https://arxiv.org/abs/2507.02881 |