Fixed point results of some nonlinear maps with applications

The main purpose of this work is to establish new coincidence and common fixed point theorems using contractive and Lipschitz type conditions for nonself single-valued and multivalued mappings (not necessarily continuous) on a metric space and cite their applications in approximation theory and eigenvalue problems. A general iteration scheme for a finite family of asymptotically quasi-nonexpansive mappings in Banach spaces is introduced and its convergence to a common fixed point of the family is studied. Random versions of these results are presented. A deep result concerning the existence of random fixed point of an inward multivalued random operator on a separable Banach space with characteristic of noncompact convexity less than 1 is also proved.