A fixed point theorem for (\phi, \shi)-convex contraction in metric spaces

Open Access

Original research article

Author(s):

Deepak Khantwal^a, Surbhi Aneja^b, U. C. Gairola^c

^aDepartment of Mathematics, Graphic Era Hill University, Dehradun, Uttarakhand, India.
^bGovernment Inter College, Punwalla Dogi, Tehri Garhwal, Uttarakhand, India.
^cDepartment of Mathematics, HNB Garhwal University, Pauri Campus, Uttarakhand, India.

Advances in the Theory of Nonlinear Analysis and its Applications 5(2), 240-245.

Received: September 3, 2020

Accepted: March 31, 2021

Published: April 4, 2021

Abstract

In the present paper, we introduce the notion of (ϕ, ψ)-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, Art. ID 406368), Rhoades (Nonlinear Anal., 47 (2001), 2683–2693), Istrăţescu (Ann. Mat. Pura Appl., 130 (1982), 89–104), and many others in the existing literature. An illustrative example is also provided to exhibit the utility of our main results.

Keywords: Fixed point, (ϕ, ψ)-weak contraction, Convex contraction, Metric space.

Share & Cite

APA Style

Khantwal, D., Aneja, S., & Gairola, U. C. (2021). A fixed point theorem for (\phi,\shi)-convex contraction in metric spaces. Advances in the Theory of Nonlinear Analysis and its Application, 5(2), 240-245.