Abstract
We extend the notion of generalized weakly contraction mappings due to Choudhury et al. (2011) to generalized α-β-weakly contraction mappings. We show with examples that our new class of mappings is a real generalization of several known classes of mappings. We also establish fixed point results for such mappings in metric spaces. Applying our new results, we obtain fixed point results on ordinary metric spaces, metric spaces endowed with an arbitrary binary relation, and metric spaces endowed with graph.
Highlights
The well-known Banach’s contraction principle has been generalized in many ways over the years [1,2,3,4,5,6]
As an application of our results, fixed point results on ordinary metric spaces, metric spaces endowed with an arbitrary binary relation, and metric spaces endowed with graph are derived from our results
We introduce the concept of generalized α-β-weakly contraction mappings and prove the fixed point theorems for such mappings
Summary
The well-known Banach’s contraction principle has been generalized in many ways over the years [1,2,3,4,5,6]. One of the most interesting studies is the extension of Banach’s contraction principle to a case of weakly contraction mappings which was first given by Alber and Guerre-Delabriere [7] in Hilbert spaces. In 2011, Choudhury et al [15] generalized weakly contraction mappings by using an altering distance control function and proved fixed point theorem for a pair of these mappings. Some generalizations of this function of fixed point problems in metric and probabilistic metric spaces have been studied [16,17,18]. As an application of our results, fixed point results on ordinary metric spaces, metric spaces endowed with an arbitrary binary relation, and metric spaces endowed with graph are derived from our results
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
