Some best proximity point results and an application to nonlinear integral equations on partial metric spaces

Abstract

In this paper, using Bianchini-Grandolfi gauge functions, we define a new notion of BG-contraction mapping and proximal BG-contraction mapping. After that, we prove some best proximity point results. Hence, we generalize and improve results existing in the literature such as [12]. Also, we provide nontrivial example to demonstrate the effectiveness of our result. Finally, we give an existence and uniqueness result for the solution of nonlinear Freldhom and Volterra integral equations via our result.

Subject Classification:

• Primary 54H25
• Secondary 47H10

Keywords:

• Best proximity point
• Bianchini-Grandolfi gauge function
• Partial metric space