Some fixed point theorems on nonlinear contractive mappings in Hilbert space - Namana Seshagiri Rao; Karusala Kalyani (E-Journal of Analysis and Applied Mathematics)
The purpose of this paper is to establish the existence and uniqueness of a common fixed point for a pair of continuous self mappings over a closed subset of Hilbert space satisfying certain nonlinear rational type contraction condition. Further this result is extended and generalized for some positive integers powers of a pair of continuous self mappings and then is devolved for a sequence of continuous self mappings in the Hilbert space. Our results generalize and extend many well known results in the literature.