- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 5 Issue: 2
- A fixed point theorem for (\phi, \shi)-convex contraction in metric spaces
A fixed point theorem for (\phi, \shi)-convex contraction in metric spaces
Authors : Deepak KHANTWAL, Surbhi ANEJA, U.c. GAİROLA
Pages : 240-245
Doi:10.31197/atnaa.735372
View : 4 | Download : 2
Publication Date : 2021-06-30
Article Type : Research
Abstract :In the present paper, we introduce the notion of (\phi, \shi)-convex contraction mapping of order m and establish a fixed point theorem for such mappings in complete metric spaces. The present result extends and generalizes the well known result of Dutta and Choudhary (Fixed Point Theory Appl. 2008 (2008), Art. ID 406368), Rhoades (Nonlinear Anal., 47(2001), 2683-2693), Istratescu (Ann. Mat. Pura Appl., 130(1982), 89-104) and besides many others in the existing literature. An illustrative example is also provided to exhibit the utility of our main results.Keywords : Fixed Point, (phi shi)-weak contraction, convex contraction, metric space