Abstract:
In this paper, we introduce the concept of $T_\beta$-contraction for a pair of commuting self-mappings and prove a common fixed point theorem for this type.
Our results improve and extend many existing results in the literature.
The paper also contains an application for non-linear integral equations.
Keywords:fixed point, $T_\beta$-contraction, $T-\alpha$-admissible, $\tau$-distance.