Fixed Point Theorems for Generalized Contractions with Triangular $\alpha$-Orbital Admissible Mappings on Branciari Metric Spaces

Abstract

The fixed point theorems and unique common fixed point theorems for generalized contractions with triangular $f$-$\alpha$-admissible mappings on Branciari metric spaces are proven omitting some conditions of $\psi \in \Psi_1$ using $\Psi_2$ the set of all nondecresing and continuous functions. We prove the unique common fixed point theorem for generalized contractions in the setting of partially ordered Branciari metric spaces using our main result. Moreover, we also present the example that supports our main result.