Weakly Compatible Mappings and Common Fixed Points Under Generalized Contractive Conditions
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| Format: | Preprint |
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2025
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| _version_ | 1866912458752393216 |
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| author | Negash, Alemayehu Bogale, Meaza |
| author_facet | Negash, Alemayehu Bogale, Meaza |
| contents | This paper establishes new common fixed point theorems for weakly compatible mappings in metric spaces, relaxing traditional requirements such as continuity, compatibility, and reciprocal continuity. We present a unified framework for three self-mappings $T$, $f$, and $g$ with a contractive condition involving a control function $ψ$, along with corollaries extending results to pairs of mappings and upper semi-continuous control functions. Further generalizations include iterated mappings and sequences of mappings. Rigorous examples demonstrate the necessity of hypotheses and show our results strictly generalize theorems by Al-Thagafi \emph{et. al.} \cite{Al-Thagafi2006}, Babu \emph{et. al.} \cite{Babu2007}, Jungck \cite{Jungck1976,Jungck1986}, Singh \cite{Singh1986,Singh1997a}, Som \cite{Som2003}, Song \cite{Song2007} and Zhang \emph{et. al.} \cite{Zhang2008}. Key advancements include eliminating completeness assumptions on the entire space and relaxing mapping compatibility conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_00035 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weakly Compatible Mappings and Common Fixed Points Under Generalized Contractive Conditions Negash, Alemayehu Bogale, Meaza General Mathematics 47H10, 54H25 This paper establishes new common fixed point theorems for weakly compatible mappings in metric spaces, relaxing traditional requirements such as continuity, compatibility, and reciprocal continuity. We present a unified framework for three self-mappings $T$, $f$, and $g$ with a contractive condition involving a control function $ψ$, along with corollaries extending results to pairs of mappings and upper semi-continuous control functions. Further generalizations include iterated mappings and sequences of mappings. Rigorous examples demonstrate the necessity of hypotheses and show our results strictly generalize theorems by Al-Thagafi \emph{et. al.} \cite{Al-Thagafi2006}, Babu \emph{et. al.} \cite{Babu2007}, Jungck \cite{Jungck1976,Jungck1986}, Singh \cite{Singh1986,Singh1997a}, Som \cite{Som2003}, Song \cite{Song2007} and Zhang \emph{et. al.} \cite{Zhang2008}. Key advancements include eliminating completeness assumptions on the entire space and relaxing mapping compatibility conditions. |
| title | Weakly Compatible Mappings and Common Fixed Points Under Generalized Contractive Conditions |
| topic | General Mathematics 47H10, 54H25 |
| url | https://arxiv.org/abs/2507.00035 |