Abstract

In this paper, we introduce the notion of modified generalized $\alpha-\psi-$Geraghty contraction type maps in the context of metric space and establish some fixed point theorems for such maps. Our results provide the fixed point results of K. Anthony Singh [8] and Popescu [16] as direct corollaries. Some examples are also given to illustrate the validity of our results.

Keywords and Phrases

Metric space, fixed point, $\alpha-$orbital admissible mapping with respect to $\eta$, triangular $\alpha-$orbital admissible mapping with respect to $\eta$ , generalized $\alpha-$Geraghty contraction type map, extended generalized $\alpha-\psi-$Geraghty contraction type map, modified generalized $\alpha-\psi-$Geraghty contraction type map.

A.M.S. subject classification

47H10, 54H25.

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