A generalized coincidence point index

Nasreddine Mohamed Benkafadar; M. C. Benkara-Mostefa

doi:10.4995/agt.2005.1959

Authors

Nasreddine Mohamed Benkafadar University of Constantine
M. C. Benkara-Mostefa University of Constantine

DOI:

https://doi.org/10.4995/agt.2005.1959

Keywords:

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

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.

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Author Biographies

Nasreddine Mohamed Benkafadar, University of Constantine

Department of Mathematics, Faculty of Sciences

M. C. Benkara-Mostefa, University of Constantine

Department of Mathematics, Faculty of Sciences

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