The Maia fixed point theorem is one of the interesting generalizations of the well-known Banach contraction principle. In this manuscript, we introduce two notions called mixed $UC-$property and mixed $P-$property of a pair $(A,B)$ of nonempty subsets of a set $X$ endowed with two metrics. First, we consider a cyclic mapping $T: A\cup B \rightarrow A\cup B$, where A and B are nonempty subset of a set $X$ endowed with two metrics, and using the mixed UC Property we obtain sufficient conditions for the existence of best proximity points of T. When A=B, then our result reduces to the Maia's fixed point theorem. Secondly, we consider a nonself mapping $T: A \rightarrow B$, where A and B are nonempty subset of a set $X$ endowed with two metrics, and using mixed P-property we obtained sufficient conditions for the existence of best proximity points of $T$. Thus, we present two best proximity point theorems which generalize the Maia fixed point theorem.
Vaithilingam, S. R., & K, A. (2024). Best Proximity Point Theorems for Maia-Type Contraction Mappings. Electronic Journal of Mathematical Analysis and Applications, 12(2), 1-8. doi: 10.21608/ejmaa.2024.287943.1191
MLA
Sankar Raj Vaithilingam; ANISHA K. "Best Proximity Point Theorems for Maia-Type Contraction Mappings", Electronic Journal of Mathematical Analysis and Applications, 12, 2, 2024, 1-8. doi: 10.21608/ejmaa.2024.287943.1191
HARVARD
Vaithilingam, S. R., K, A. (2024). 'Best Proximity Point Theorems for Maia-Type Contraction Mappings', Electronic Journal of Mathematical Analysis and Applications, 12(2), pp. 1-8. doi: 10.21608/ejmaa.2024.287943.1191
VANCOUVER
Vaithilingam, S. R., K, A. Best Proximity Point Theorems for Maia-Type Contraction Mappings. Electronic Journal of Mathematical Analysis and Applications, 2024; 12(2): 1-8. doi: 10.21608/ejmaa.2024.287943.1191
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