New best proximity point results on orthogonal F-proximal contractions with applications

Abstract

In this work, we propose the ideas of orthogonal $F$-proximal contraction mappings, generalized orthogonal $F$-proximal contraction mappings and establish several best proximity point theorems in an orthogonally complete metric space ($\mathrm{OCMS}$) through a non-self mapping. Hence, utilizing these recently discovered results, numerous of the existing findings in the literature are generalized or expanded. An illustration is provided to highlight the utility of our findings. Finally, for illustrative applications, we discuss the qualitative properties of the solutions for a fractional boundary value problem in the Caputo sense, and we study the dynamic economic equilibrium problem.