Journal of Advanced Analysis and Applications
Volume 1, Issue 1 (2026), Pages 69–92

Functional Contractions in Relational Metric Spaces
Author: Mihai Turinici

A. Myller Mathematical Seminar, A. I. Cuza University, 700506 Iaşi, Romania
Email: mturi@uaic.ro

Abstract. The 2015 fixed point result on rs-relational metric spaces, due to Alam and Imdad
[J. Fixed Point Theory Appl. 17 (2015), 693–702], is equivalent to the classical Banach contraction
principle [Fund. Math. 3 (1922), 133–181]. The same is true for the 1961 statement in metric spaces,
due to Edelstein [Proc. Amer. Math. Soc. 12 (1961), 7–10], and for the 2005 fixed point result in
quasi-ordered metric spaces obtained by Nieto and Rodríguez-López [Order 22 (2005), 223–239].

Keywords: relational metric space; monotone mapping; fixed point; global strongly Picard operator;
Banach contraction principle

MSC (2020): 47H10, 54H25

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Submitted: April 22, 2026 / Accepted: May 15, 2026 / Published: May 16, 2026

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How to cite: M. Turinici, Functional contractions in relational metric spaces,
Journal of Advanced Analysis and Applications, 1(1) (2026), 69–92.
DOI: https://doi.org/10.66745/jaaa.v1i1.005

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