Hypergraphical Metric Spaces and Fixed Point Theorems

Abstract

Hypergraph is a generalization of graph in which an edge can join any number of vertices. Hypergraph is used for combinatorial structures which generalize graphs. In this research work, the notion of hypergraphical metric spaces is introduced, which generalizes many existing spaces. Some fixed point theorems are studied in the corresponding spaces. To show the authenticity of the established work, nontrivial examples and applications are also provided.

Fixed-Point Results for Generalized Rational Contractions in Graphical b-Metric Spaces with Applications

“…Ten, it is very simple to prove that (M, d gb ) is a graphical b-metric space with coefcient s � 3/2, where G � (V(G), E(G)) and V(G) � M and E(G) as shown in Figure 1. Notice that it is not a graphical metric space because For more characteristics in the direction of graphic contractions, graphical metric spaces, and graphical b-metric spaces, we refer the readers to [10][11][12][13][14][15][16][17][18][19][20][21].…”