Abstract

A theorem on the zero existence preservation for a parametric family of multivalued (α, β)-search functionals on an open subset of a metric space is proved. Several corollaries on the existence preservation for preimages of a closed subspace, for coincidence points, and for common fixed points under the action of a parametric family (a number of families) of mappings are obtained. The notion of a Zamfirescu-type pair of mappings is introduced, and a coincidence theorem for such pairs of mappings is obtained. In addition, a theorem on the coincidence existence preservation for a parametric family of such pairs of mappings is obtained. The obtained results imply several well-known theorems.

中文翻译：

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一类多值泛函的零保存及其在不动点和重合理论中的应用

摘要

证明了在度量空间的一个开放子集上的多值（α，β）-搜索函数的参数族的零存在保留的定理。在封闭的子空间的原像，重合点和在映射的参数族（多个族）的作用下对于公共不动点的存在保存方面，获得了一些推论。介绍了Zamfirescu型映射对的概念，并获得了此类映射对的重合定理。另外，获得了关于这种映射对的参数族的重合存在保持性的定理。获得的结果暗示了几个众所周知的定理。