ИСТИНА

The talk is based on several works listed below. We give the zero existence principle for so called (,)-search functionals on a metric space proposed earlier by the author [1,2]. Recently, in our joint work with Yu. N. Zakharyan [3], we obtained a parametric version of this principle. More exactly, we considered the problem of the zero existence preservation in a family of (,)-search functionals, under the changing of a numerical parameter. These results imply some new fixed point and coincidence existence theorems for multivalued mappings of metric (and some generalized metric) spaces [4]. In addition, the obtained results imply generalizations and parametric versions of some known theorems. In particular, a parametric version of the well-known Michiel selection theorem is obtained [5]. As well, we’ll concern in the talk some other applications of the mentioned results. For example, an application to the problem of the equilibrium strategy existence preservation in a parametric family of antagonistic games with two players.