Geraghty and Ćirić type fixed point theorems in b-metric spaces

Abstract

In this paper, we obtain some fixed point theorems for admissible mappings in b-metric spaces. Some useful examples are given to illustrate the facts. We also discuss an application to a nonlinear quadratic integral equation. Our results complement, extend and generalize a number of fixed point theorems including the well-known Geraghty [M. A. Geraghty, Proc. Amer. Math. Soc., 40 (1973), 604–608] and Ćirić [L. B. Ćirić, Proc. Amer. Math. Soc., 45 (1974), 267–273] theorems on b-metric spaces.