@article{article_735372, title={A fixed point theorem for (\phi, \shi)-convex contraction in metric spaces}, journal={Advances in the Theory of Nonlinear Analysis and its Application}, volume={5}, pages={240–245}, year={2021}, DOI={10.31197/atnaa.735372}, author={Khantwal, Deepak and Aneja, Surbhi and Gairola, U.c.}, keywords={Fixed Point, (\phi \shi)-weak contraction, convex contraction, metric space}, 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.}, number={2}, publisher={Erdal KARAPINAR}