Fixed Point Theorems for Modified (alpha-psi-varphi-theta)-Rational Contractive Mappings in alpha-Complete b-Metric Spaces: Anchalee Kaewcharoen, Preeyaluk Chuadchawna - Team, Support (Thai Journal of Mathematics, 2016)
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 α-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.