Common Fixed Point Theorems Of Weakly Compatible Maps Satisfying (f,g)-Weakly Contractive Condition And Invariant Approximation Results
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| Format: | Preprint |
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2025
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| _version_ | 1866911218383454208 |
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| author | R., Babu G. V. D, Ratna Babu Negash, Alemayehu |
| author_facet | R., Babu G. V. D, Ratna Babu Negash, Alemayehu |
| contents | We prove the existence of common fixed points for three selfmaps $T,f$ and $g$ defined on a metric space $(X,d)$ satisfying, $T$ is $(f,g)$-weakly contractive; and the pairs $(T,f)$ and $(T,g)$ are weakly compatible. Also, for such $T,f$ and $g$, we prove the convergence of modified Mann iteration and modified Ishikawa iteration with respect to $T,f$ and $g$ to their common fixed point, in a normed space. Further, we obtain invariant approximation results from the set of best approximations to common fixed points of $T,f$ and $g$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_16268 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Common Fixed Point Theorems Of Weakly Compatible Maps Satisfying (f,g)-Weakly Contractive Condition And Invariant Approximation Results R., Babu G. V. D, Ratna Babu Negash, Alemayehu Dynamical Systems 47H10, 54H25 We prove the existence of common fixed points for three selfmaps $T,f$ and $g$ defined on a metric space $(X,d)$ satisfying, $T$ is $(f,g)$-weakly contractive; and the pairs $(T,f)$ and $(T,g)$ are weakly compatible. Also, for such $T,f$ and $g$, we prove the convergence of modified Mann iteration and modified Ishikawa iteration with respect to $T,f$ and $g$ to their common fixed point, in a normed space. Further, we obtain invariant approximation results from the set of best approximations to common fixed points of $T,f$ and $g$. |
| title | Common Fixed Point Theorems Of Weakly Compatible Maps Satisfying (f,g)-Weakly Contractive Condition And Invariant Approximation Results |
| topic | Dynamical Systems 47H10, 54H25 |
| url | https://arxiv.org/abs/2510.16268 |