On (G, G′)-Prešić–Ćirić Operators in Graphical Metric Spaces

Abstract

The purpose of this paper is to introduce a new type of operators in graphical metric spaces and to prove some fixed point results for these operators. Several known results are generalized and extended in this new setting of graphical metric spaces. The results are illustrated and justified with examples.

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

“…As the sequence ϑ n 􏼈 􏼉 is a H G -TWC sequence and G is a subgraph of G, so by using inequality (14) and the triangular inequality, we have (15), we have…”

“…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].…”

A NEW FIXED POINT RESULT IN GRAPHICAL bv(s)-METRIC SPACE WITH APPLICATION TO DIFFERENTIAL EQUATIONS

“…A connected component of the graph G is a connected sub-graph G 1 of a graph G such that there is no path between vertices of G 1 and vertices of G\G 1 . For more information we refer reader to [4,5,9,16,17].…”

On a Unique Solution of a T-Maze Model Arising in the Psychology and Theory of Learning

“…It has been generalized and extended in various directions (for the detail, see [13][14][15][16]). For more details about the fixed point theory and its applications in different spaces, we refer the reader to [17][18][19][20][21][22].…”