Advanced Generalizations of Weighted Opial-Type Inequalities in the Framework of Time Scale Calculus

Axioms 2026 Open access

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Authors: Nadiah Zafer Al-Shehri, Mohammed M. A. El-Sheikh, Mohammed Zakarya, Hegagi M. Ali, Haytham M. Rezk, Fatma M. Khamis
DOI: 10.3390/axioms15010046
Cited by: 2
References: 11

Abstract

This work presents refined and generalized forms of weighted Opial-type inequalities within the framework of time scale calculus. The proofs rely on several algebraic techniques, together with Hölder’s inequality and Keller’s chain rule. These results extend the classical Opial-type inequalities by embedding them into the time scale setting, which unifies both continuous and discrete analyses. Consequently, various integral and discrete inequalities emerge as particular cases of our main results, thereby broadening the applicability of Opial-type inequalities to dynamic systems and discrete models.

Fields of Study & Subjects

Nonlinear Differential Equations Analysis Contact Mechanics and Variational Inequalities Mathematics and Applications

Publication details

Journal / source
Axioms
Publisher
MDPI AG
Volume
15
Issue
1
Pages
46–46
Publication date
8 January 2026
Language
EN