Vol. 9(1) Jan. 2021, No. 15, pp. 174-178.

SOME REMARKS ON THE PAPER “FIXED POINT OF α-GERAGHTY CONTRACTION WITH APPLICATIONS”
Vol. 9(1) Jan. 2021, No. 15, pp. 174-178
K. ANTHONY SINGH

 

Abstract

Muhammad Arshad, Aftab Hussain and Akbar Azam (Fixed point of α-Geraghty contraction with applications, U.P.B. Sci. Bull., Series A, Vol. 78, Iss. 2, 2016) improved the notion of α-Geraghty contraction type mappings and established some common fixed point theorems for a pair of α-admissible mappings under the improved notion of α-Geraghty contraction type condition in a complete metric space. But we observe some gaps in the proof of some theorems in the paper due to some insufficiency in the defining condition of the associated contraction mappings. The aim of this paper is to attempt to bridge the gaps by proposing some modifications in the contraction condition of the mappings.


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