Zeros of conic functions, fixed points, and coincidences

The concept of a conic function with operator coefficients on a conic metric space is introduced. A zero existence theorem is proved for such functions. On this basis, a fixed point theorem for a multivalued self-mapping of a conic metric space is obtained, which generalizes the recent fixed point theorem of E.S. Zhukovskiy and E.A. Panasenko for a contracting multivalued mapping of a conic metric space with an operator contracting coefficient. Coincidence theorems for two multivalued mappings of conic metric spaces are obtained, which generalize the author’s previous results on coincidences of two multivalued mappings of metric spaces.