Search for Zeros of Functionals, Fixed Points, and Mappings Coincidence in Quasi-Metric Spaces

Abstract

The cascade search principle for zeros of (α, β)-search functionals and consequent fixed point and coincidence theorems are proved for collections of single-valued and set-valued mappings of (b₁, b₂)-quasimetric spaces. These results are extensions of previous author’s results for metric spaces. In particular, a generalization is obtained for the recent result on coincidences of a covering mapping and a Lipschitz mappings of (b₁, b₂)-quasimetric spaces.