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

Authors : Deepak KHANTWAL, Surbhi ANEJA, Uc GAİROLA

Pages : 240-245

Doi:10.31197/atnaa.735372

View : 9 | Download : 7

Publication Date : 2021-06-30

Article Type : Research Paper

Abstract :In the present paper, we introduce the notion of insert ignore into journalissuearticles values(\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 insert ignore into journalissuearticles values(Fixed Point Theory Appl. 2008 insert ignore into journalissuearticles values(2008);, Art. ID 406368);, Rhoades insert ignore into journalissuearticles values(Nonlinear Anal., 47insert ignore into journalissuearticles values(2001);, 2683-2693);, Istratescu insert ignore into journalissuearticles values(Ann. Mat. Pura Appl., 130insert ignore into journalissuearticles values(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