Zeros of conic functions, fixed points and coincidences

Concept of conic function with operator coefficients is introduced. Zero existence theorem is proved for such functions. On this basis, fixed point theorem is obtained, for a multivalued self-mapping of a conic metric space, generalizing the recent fixed point theorem by E.S. Zhukovsky and E.A. Panasenko, for a contracting multivalued mapping of a conic metric space, with operator contracting coefficient. Coincidence theorems are obtained, for two multivalued mappings of conic metric spaces, which generalize the more previous author's results on coincidences of two multivalued mappings of metric spaces.