A Generalisation of Contraction Principle in Metric Spaces

Abstract

Here we introduce a generalisation of the Banach contraction mapping principle. We show that the result extends two existing generalisations of the same principle. We support our result by an example.

Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces

“…Since a b-metric is a metric when s = 1, so our results can be viewed as the generalization and extension of corresponding results in [10,11,24] and several other comparable results. …”

“…A self-mapping f on X is said to be weakly contractive if Dutta and Choudhury [11] generalized the weak contractive condition and proved the following fixed point theorem which in turn extends Theorem 1.3 and the corresponding result in [3].…”

Fixed point theorems on ordered gauge spaces with applications to nonlinear integral equations

“…Then T has a unique fixed point. Dutta and Choudhury [20] present a generalization of Theorems 1.2 and 1.4 proving the following result. Theorem 1.5 (Dutta and Choudhury [20]) Let (X, d) be a complete metric space and T : X X be a mapping satisfying…”

The Existence of Fixed Points for Generalized Weak Contractions

“…Therefore Φ-contraction is weaker than φ-weak contraction above. In 2008, Dutta and Choudhury [4] gave the following the existence theorem of fixed points for φ-weak contractions. If one takes ψ(t) = t for t ∈ [0, +∞) in Theorem 1.3, then it reduces to Corollary 2.2 of Zhang et al [5].…”