Mohammed Mohammed Taleb - Department of Mathematics, Science College, Swami Ramanand Teerth Marathwada University, Nanded-۴۳۱۶۰۶, India.
V. Borkar - Department of Mathematics, Yeshwant Mahavidyalaya, Swami Ramanand Teerth Marathwada University, Nanded-۴۳۱۶۰۶, India.

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.

Fixed point, (ϕ, ψ)-metric space, Generalized (ϕ, σ, γ)-rational contraction, Generalized (α, β, ϕ, θ, F)-rational contraction, First order differential equations