A Relation Theoretic Approach for φ-Fixed Point Result in Metric Space with an Application to an Integral Equation

Document Type: Original Article


1 Department of Applied Mathematics & Humanities, S. V. National Institute of Technology, Surat-395007, Gujarat, India

2 Poornima College of Engineering, Jaipur-302022, Rajasthan, India


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 for
those elements that are related under the binary relation and not for the whole space. An application is
given to show the φusability of our result obtained.


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