Abstract

Recently, Erdal Karapinar ([8] Karapinar E., $\alpha-\psi-$Geraghty contraction type mappings and some related fixed point results, Filomat, 28:1 37-48 (2014)) introduced the notion of generalized $\alpha-\psi-$Geraghty contraction type mappings in the setting of a metric space and proved the existence and uniqueness of a fixed point of such mappings. But we observe that the condition (H1) for the uniqueness of the fixed point of such mappings as proposed by Karapinar is not enough. The aim of this paper is to attempt to rectify it by proposing a slightly stronger condition in place of condition (H1).

Keywords and Phrases

Metric space, fixed point, $\alpha-$admissible map, triangular $\alpha-$admissible map, generalized $\alpha-\psi-$ Geraghty contraction type mapping.

A.M.S. subject classification

Primary: 46T99; Secondary: 47H10, 54H25, 46J10, 46J15.

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