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A Generalization of Contraction Principle

Author(s):

Sujata Goyal , A.S.COLLEGE KHANNA

Keywords:

Fixed Point, Altering Distance Function, Weakly Contractive Map

Abstract

Dutta and Choudhury [1] proved the following result: If (X, d) is a complete metric space and T : X→X a self-mapping satisfying the inequality Ψ(d(Tx, Ty))≤ ψ(d(x, y)−φ(d(x, y) where ψ, φ : [0,∞) →[0,∞) are both continuous and monotone non-decreasing functions with ψ(t)= φ(t) = 0 if and only if t = 0. Then T has a unique fixed point. In this paper, we have proved that if we do not assume the conditions of continuity on both ψ and φ, still the result is valid.

Other Details

Paper ID: IJSRDV5I50196
Published in: Volume : 5, Issue : 5
Publication Date: 01/08/2017
Page(s): 228-229

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