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.

中文翻译：

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在拟度量空间中搜索泛函，固定点和映射重合的零点

对于（b ₁，b ₂）拟空间的单值集和集值映射的集合，证明了（α，β）搜索泛函的零级联搜索原理以及由此产生的不动点和重合定理。这些结果是先前作者对度量空间的结果的扩展。特别地，获得了关于（b ₁，b ₂）拟空间的覆盖映射和Lipschitz映射的重合的最新结果的概括。