A Novel Fixed Point Theorem of Reich-Perov Type α−Contractive Mapping in Vector-Valued Metric Spaces

Abstract

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.

Key words and phrases. Reich-Perov contractive mapping; Reich-Perov α-contractive mapping; α-admissible; fixed point.

2010 Mathematics Subject Classification. 47H10, 54H25