A New Best Proximity Point Results in Partial Metric Spaces Endowed with a Graph

Abstract

For a given mapping f in the framework of different spaces, the fixed-point equations of the form fx=x can model several problems in different areas, such as differential equations, optimization, and computer science. In this work, the aim is to find the best proximity point and to prove its uniqueness on partial metric spaces where the symmetry condition is preserved for several types of contractive non-self mapping endowed with a graph. Our theorems generalize different results in the literature. In addition, we will illustrate the usability of our outcomes with some examples. The proposed model can be considered as a theoretical foundation for applications to real cases.

Keywords

• proximity point
• partial metric spaces
• <i>G</i>-contraction
• connected graph