Fixed Point Theorems with Respect to a c-Distance in Cone Metric Spaces Endowed with a Graph

Fatemeh Anousheh, Ghasem Soleimani Rad

Abstract

In this paper we study the existence of the fixed points for mappings with respect to a $c$-distance in cone metric spaces endowed with a graph. Our results are significant, since we need to use neither the continuity of mapping nor the normality of cone and provide a more general statement of Rahimi and Soleimani Rad [H. Rahimi, G. Soleimani Rad, Note on ``Common fixed point results for noncommuting mappings without continuity in cone metric spaces", Thai J. Math. 11 (2013) 589-599] and Kaewkhao et al. [A. Kaewkhao, W. Sintunavarat, P. Kumam, Common fixed point theoremsof $c$-distance on cone metric spaces, J. Nonlinear Anal. Appl. 2012 (2021) Article ID jnaa-00137].