A discussion on generalized almost contractions via rational expressions in partially ordered metric spaces

Abstract

The main purpose of this paper is to give some fixed point results for mappings involving generalized (Formula presented.)-contractions in partially ordered metric spaces. Our results generalize, extend, and unify several well-known comparable results in the literature (Jaggi in Indian J. Pure Appl. Math. 8(2):223-230, 1977, Harjani et al. in Nonlinear Anal. 71:3403-3410, 2009, Luong and Thuan in Fixed Point Theory Appl. 2011:46, 2011). The presented results are supported by three illustrative examples. MSC: 46N40, 47H10, 54H25, 46T99.