Coupled ‎f‎ixed points for a class of non-cyclic contractions in uniformly convex Banach spaces with error estimates

Document Type : Research Article

Authors

Akram Safari-Hafshejani

Khadije Amiri

Department of Pure Mathematics‎, ‎Payame Noor University (PNU), ‎P‎. ‎O‎. ‎Box‎: ‎19395- 3697‎, ‎Tehran‎, ‎Iran.

10.22067/ijnao.2026.98129.1861

Abstract

In this paper, we introduce a non-cyclic contraction pair of an ordered pair of mappings. We then deduce the existence and uniqueness of coupled fixed points by associating a non-cyclic contraction with them. In addition, we obtain both a priori and a posteriori error estimates for these points in uniformly convex Banach spaces. The main result is illustrated with an example, and as an application, a cyclic version of the main theorem is derived. In addition, we obtain both a priori and a posteriori error estimates for these points in uniformly convex Banach spaces. The main result is illustrated with an example, and as an application, a cyclic version of the main theorem is derived.

Keywords

Non-cyclic contraction pair

Coupled fixed point

Coupled best proximity point

A priori and a posteriori error estimates

&lrm

$UC$ property

Subjects

• Numerical Analysis

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