ABSTRACT
The classical Banach contraction principle was extended for contractive maps on spaces endowed with vector-valued metric spaces by Perov in 1964 [237], Perov and Kibenko [238] and Precup [247]. For a version of Schauder’s fixed point, see Viorel [279]. The purpose of this section is to present that version of Schaefer’s fixed point theorem and the nonlinear alternative of Leary-Schauder type in generalized Banach spaces.
