New Fixed Point Results for Some Rational Contraction on $(\phi , \psi)$-Metric Spaces

Abstract

In this article, we define generalized $(\varphi,\sigma,\gamma)$-rational contraction, generalized $(\alpha\beta,\varphi\theta,F)$-rational contraction and establish some new fixed point results in $(\phi,\psi)$-metric space. We also present instances to support our main results. We will use the results we obtained to investigate the existence and uniqueness of solutions to first-order differential equations.

Keywords

• fixed point
• (ϕ
• ψ)-metric space
• generalized (ϕ
• σ
• γ)-rational contraction
• generalized (α
• β
• ϕ
• θ
• f)-rational contraction
• first order differential equations