Some fixed point theorems on nonlinear contractive mappings in Hilbert space
Authors: Namana Seshagiri Rao, Karusala Kalyani
Journal: e-Journal of Analysis and Applied Mathematics (e-JAAM), e-ISSN 2544-9990
Volume: 2020 · Pages: 1 - 12
Published Online: 19 Jun 2020
Abstract: 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.
Keywords: Hilbert space, closed subset, Cauchy sequence, completeness