A generalized coincidence point index

N.M. Benkafadar, M.C. Benkara-Mostefa

Abstract

The paper is devoted to build for some pairs of continuous single-valued maps a coincidence point index. The class of pairs (f, g) satisfies the condition that f induces an epimorphism of the Cech homology groups with compact supports and coefficients in the field of rational numbers Q. Using this concept one defines for a class of multi-valued mappings a fixed point degree. The main theorem states that if the general coincidence point index is different from {0}, then the pair (f, g) admits at least a coincidence point. The results may be considered as a generalization of the above Eilenberg-Montgomery theorems [12], they include also, known fixed-point and coincidence-point theorems for single-valued maps and multi-valued transformations.


Keywords

Point; Concidence point; Index; Degree; Multi-valued mapping

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Topology and its Applications  vol: 268  first page: 106904  year: 2019  
doi: 10.1016/j.topol.2019.106904



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