Fixed Point Theorems for Modified (alpha-psi-varphi-theta)-Rational Contractive Mappings in alpha-Complete b-Metric Spaces

Anchalee Kaewcharoen, Preeyaluk Chuadchawna

Abstract

In this paper, we introduce the notion of  modified (alpha-psi-varphi-theta)-rational contraction mappings  where some conditions of Bianchini-Grandolfi gauge function  varphi is omitted.  We establish the existence of the unique fixed point theorems for such mappings which are triangular $\alpha$-orbital admissible in alpha complete b-metric spaces. Moreover, we also prove the unique common fixed point theorem for  mappings $T$ and $g$ where T is a  modified (alpha-psi-varphi-theta)-rational contraction mapping with respect to g. Our results extend the fixed point theorems in alpha-complete metric spaces proved by Hussian et al. [N. Hussain, M. A. Kutbi and P. Salimi, Fixed point theory in alpha-complete metric spaces with applications, Abstr. Appl. Anal., (2014) Article ID 280817] to alpha-complete b-metric spaces.