Common Fixed Point Theorems for Weakly Contractions in Rectangular b -Metric Spaces with Supportive Applications

Abstract

In this manuscript, two new classes of generalized weakly contractions are introduced and common fixed point results concerning the new contractions are proved in the context of rectangular b -metric spaces. Also, some examples are included to present the validity of our theorems. As an application, we provide the existence and uniqueness of solution of an integral equation.

Sehgal-Guseman-Type Fixed Point Theorems in Rectangular b -Metric Spaces and Solvability of Nonlinear Integral Equation

“…Meanwhile, they gave some fixed point theorems. Lately, Gulyaz-Ozyurt [17], Zheng et al [18], and Guan et al [19] also studied fixed point theory in such spaces and obtained some excellent results. In 2021, Hussain [20] presented some fractional symmetric α-η-contractions and built up some new fixed point theorems for these types of contractions in F-metric spaces.…”