OICC Press Communications in Nonlinear Analysis 2371-7920 6 1 2025 11 09 A Relation Theoretic Approach for φ-Fixed Point Result in Metric Space with an Application to an Integral Equation EN D. Gopal Department of Applied Mathematics & Humanities, S. V. National Institute of Technology, Surat-395007, Gujarat, India L. M. Budhia Department of Applied Mathematics & Humanities, S. V. National Institute of Technology, Surat-395007, Gujarat, India S. Jain Poornima College of Engineering, Jaipur-302022, Rajasthan, India Journal Article 2025 11 09 In this paper, we prove the existence and uniqueness of φ-fixed point for (F,φ,θ)-contraction mapping in a complete metric space with a binary relation. Here the contractive condition is required to hold only forthose elements that are related under the binary relation and not for the whole space. An application isgiven to show the φusability of our result obtained.