Geodesic
Method of search functionals and its applications in fixed point and coincidence theory
Contemporary Mathematics. Fundamental Directions, Contemporary Mathematics. Fundamental Directions, Tome 69 (2023) no. 1, pp. 185-200.

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The paper contains a survey of several results from the author's papers and joint papers by the author and Yu. N. Zakharyan, both on the zero existence and approximation for single-valued and multi-valued $(\alpha,\beta)$-search functionals, and also on the zero existence preservation for parametric family of such functionals, under the parameter changing. Some corollaries of these results in the fixed point and coincidence theory of single-valued and multi-valued mappings of metric spaces are also given. The comparison is provided with some known results by other authors. In the concluding part of the paper, we investigate the problem on the existence of a parameter-continuous single-valued branch of zeros for a parametric family of search functionals. A theorem on the existence of solution of this problem is proved.
Keywords: search functionals, existence of zeros, fixed points, coincidence points. 
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T. N. Fomenko. Method of search functionals and its applications in fixed point and coincidence theory. Contemporary Mathematics. Fundamental Directions, Contemporary Mathematics. Fundamental Directions, Tome 69 (2023) no. 1, pp. 185-200. http://geodesic.mathdoc.fr/item/CMFD_2023_69_1_a11/

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