Best Proximity Point Theorems for Maia-Type Contraction Mappings | ||
| Electronic Journal of Mathematical Analysis and Applications | ||
| Volume 12, Issue 2, 2024, Pages 1-8 PDF (456.58 K) | ||
| Document Type: Regular research papers | ||
| DOI: 10.21608/ejmaa.2024.287943.1191 | ||
| Authors | ||
| Sankar Raj Vaithilingam* 1; ANISHA K2 | ||
| 1Manonmaniam Sundaranar University | ||
| 2Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli 627012, Tamil Nadu, India | ||
| Abstract | ||
| 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. | ||
| Keywords | ||
| fixed point; cyclic contraction; mixed UC-Property; mixed $P-$property; best proximity point | ||
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