On new fixed point results for (α, ψ, ξ)-contractive multi-valued mappings on α-complete metric spaces and their consequences

The purpose of this paper is to establish new fixed point results for multi-valued mappings satisfying an (alpha,psi,xi)-contractive condition, and via Bianchini-Grandolfi gauge functions, on alpha-complete metric spaces. Our results unify, generalize, and complement various results from the literature. We also give examples which support our main result while previous results in the literature are not applicable. Some of the fixed point results in metric spaces endowed with an arbitrary binary relation and endowed with a graph are given here to illustrate the usability of the obtained results.