Generalization of Fixed Point Results of Contractive Maps by Altering Distances

G.V.R. Babu, P. Subhashini

Abstract

We introduce a contractive map involving an altering distance function. The class of such maps need not be continuous and it is larger than the class of contractive maps. We prove the existence of fixed points of contractive maps involving an altering distance fuction in complete metric spaces. Our results generalize the results of Geraghty [M.A. Geraghty, On contractive maps, Proc. Amer. Math. Soc. 40 (1973) 604–608] and improves a result of Sastry et al. [K.P.R. Sastry, G.V.R. Babu, M.V.R. Kameswari, Fixed points of strip ϕ-contractions, Mathematical Communications 14 (2) (2009) 183–192]. Examples are provided in support of our results.