A NOVEL FIXED POINT THEOREM OF REICH-PEROV TYPE α-CONTRACTIVE MAPPINGS IN VECTOR-VALUED METRIC SPACES

This article discusses a novel concept of Reich-Perov type α-contractive mappings in vector-valued metric spaces. First, we define Reich-Perov-type contractive mappings using a novel concept in vector-valued metric spaces. Later, we investigate the sufficient conditions for a Reich-Perov type contractive mapping to have a unique fixed point in the spaces. By defining an α-contractive mapping, we next show the sufficient conditions of the existence and uniqueness of a fixed point of the Reich-Perov type α-contractive mappings in vector-valued metric spaces.