On coincidence point and fixed point theorems for nonlinear multivalued maps

Several characterizations of MT -functions are first given in this paper. Applying the characterizations of MT -functions, we establish some existence theorems for coincidence point and fixed point in complete metric spaces. From these results, we can obtain new generalizations of Berinde–Berindeʼs fixed point theorem and Mizoguchi–Takahashiʼs fixed point theorem for nonlinear multivalued contractive maps. Our results generalize and improve some main results in the literature.