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Fixed points of Kannan contractive mappings in relational metric spaces. (English) Zbl 1468.54063

Summary: In this paper, we prove an analogous version of fixed point theorem due to R. Kannan [Bull. Calcutta Math. Soc. 60, 71–76 (1968; Zbl 0209.27104)] via conditional contractive mappings and some other relational metrical notions. In the proof of present results, we utilize the notion of comparable mappings and some other well known classical fixed point theorems in the settings of relational and ordered metric spaces. We also, highlight the close connection of \(\alpha\)-admissible mappings with the binary relation and partial order relation as well. Radically, these investigations open another new direction of metric fixed point theory for contractive type mappings. Moreover, non-trivial examples are given to demonstrate the importance and usefulness of such findings.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces
54E50 Complete metric spaces

Citations:

Zbl 0209.27104
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Full Text: DOI

References:

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