Fixed point theorems to generalize FR- contraction mappings with application to nonlinear matrix equations

Authors : Deepak KHANTWAL, Swati ANTAL, Uc GAİROLA

Pages : 631-652

Doi:10.31801/cfsuasmas.793098

View : 13 | Download : 10

Publication Date : 2021-12-31

Article Type : Research Paper

Abstract :In the present paper, we introduce the notion of generalize FR-contraction and establish some fixed point results for such mappings, which extend and generalize the result of Alam and Imdad insert ignore into journalissuearticles values(J. Fixed Point Theory & Appl., 17insert ignore into journalissuearticles values(4); insert ignore into journalissuearticles values(2015);, 693-702);, Sawangsup et al. insert ignore into journalissuearticles values(J. Fixed Point Theory, 2016 insert ignore into journalissuearticles values(2016);, 1-15); and many others. Our results reveal that the assumption of M-closedness of underlying binary relation is not necessary condition for existence of fixed point in relational metric spaces. We also derive some N-order fixed point theorems from our main results. As an application of our main result, we find a solution of a certain class of nonlinear matrix equations.
Keywords : Fixed point, contraction mapping, binary relation, k continuous mapping