FIXED POINT RESULTS FOR HARDY-ROGERS TYPE CONTRACTIONS WITH RESPECT TO A 𝐶-DISTANCE IN GRAPHICAL CONE METRIC SPACES

Abstract

The aim of this paper is to prove some existence and uniqueness results of the fixed points for Hardy-Rogers type contraction in cone metric spaces associated with a 𝑐-distance and endowed with a graph. These results prepare a more general statement, since we apply the condition of orbitally 𝐺-continuity of mapping instead of the condition of continuity, and consider cone metric spaces endowed with a graph instead of cone metric spaces.

Keywords

• 𝑐-distance
• cone metric spaces
• fixed point
• orbitally 𝐺-continuous
• connected graph