Fixed Point Results for (α, η, ψ, ξ)-Contractive Multi-Valued Mappings in Menger PM-Spaces and their Applications

Abstract

In this paper, we obtain some new fixed point theorems for $(\alpha,\eta,\psi,\xi)$-contractive multi-valued mappings in $\alpha$-$\eta$-$\mathscr {T}$-complete Menger PM-spaces, which turn out to generalize many results in existing literatures. Some examples are also given to illustrate the definition and support our new results. Moreover, some interesting fixed point results endowed with binary relations or graphs are derived as applications of our main results.