Delta Calculus on Time Scale Formulas That Are Similar to Hilbert-Type Inequalities

Haytham M. Rezk, Juan E. Nápoles Valdés (), Maha Ali, Ahmed I. Saied and Mohammed Zakarya
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Haytham M. Rezk: Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City 11884, Egypt
Juan E. Nápoles Valdés: Facultad de Ciencias Exactas y Naturales y Agrimensura, Universidad Nacional del Nordeste, Av. Libertad 5450, Corrientes 3400, Argentina
Maha Ali: Department of Mathematics, College of Arts and Sciences, King Khalid University, P.O. Box 64512, Abha 62529, Sarat Ubaidah, Saudi Arabia
Ahmed I. Saied: Department of Mathematics, Faculty of Science, Benha University, Benha 13511, Egypt
Mohammed Zakarya: Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia

Mathematics, 2023, vol. 12, issue 1, 1-16

Abstract: In this article, we establish some new generalized inequalities of the Hilbert-type on time scales’ delta calculus, which can be considered similar to formulas for inequalities of Hilbert type. The major innovation point is to establish some dynamic inequalities of the Hilbert-type on time scales’ delta calculus for delta differentiable functions of one variable and two variables. In this paper, we use the condition a j ( s j ) = 0 and a j ( s j , z j ) = a j ( w j , n j ) = 0 , ∀ j = 1 , 2 , … , n . These inequalities will be proved by applying Hölder’s inequality, the chain rule on time scales, and the mean inequality. As special cases of our results (when T = N and T = R ), we obtain the discrete and continuous inequalities. Also, we can obtain other inequalities in different time scales, like T = q Z − , q > 1 .

Keywords: Hilbert-type inequalities; Hölder’s inequality; mean inequality; kernels; delta integrals; time scales (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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