DOI: 10.24193/fpt-ro.2022.1.17

Authors: Md Hasanuzzaman, Mohammad Imdad and Hayel N. Saleh

Abstract: In this paper, we introduce the idea of 𝓛_ℛ-contraction by employing an amorphous binary relation on 𝓛-contraction in a metric space. We prove an existence and corresponding uniqueness fixed point results for 𝓛_ℛ-contraction employing an S-transitive binary relation on metric spaces without completeness and also furnish an illustrative example to demonstrate the utility of our main results. Finally, we apply our newly obtained results to show the existence of a non-negative solution of the first-order ordinary differential equation.

Key Words and Phrases: Fixed points, 𝓛_ℛ-contraction, binary relations, differential equation.

2010 Mathematics Subject Classification: 47H10, 54H25.

Published on-line: February 1st, 2022.

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