DOI: 10.24193/fpt-ro.2021.2.46

Authors: S. Karmakar, H. Garai, L.K. Dey and A. Chanda

Abstract: In this article, we introduce the notions of F-contractions and Hardy-Rogers type F-contractions via w-distances in the backdrop of an orthogonal metric space. After this, we prove some fixed point results concerning the said kind of contractions by taking a weaker version of completeness of the underlying space instead of completeness. Further, we employ the results to obtain some existence and uniqueness criteria of the solution(s) to a certain type of second order initial value and boundary value problems. Along with these, we illustrate some numerical examples to interpret our achieved fixed point results.

Key Words and Phrases: F-contractions, w-distances, orthogonal metric spaces, second order differential equations.

2010 Mathematics Subject Classification: 47H10, 54H25, 34A12, 34B15.

Published on-line: July 1st, 2021.

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