Rezk, H.M.; Valdés, J.E.N.; Ali, M.; Saied, A.I.; Zakarya, M. Delta Calculus on Time Scale Formulas That Are Similar to Hilbert-Type Inequalities. Mathematics2024, 12, 104.
Rezk, H.M.; Valdés, J.E.N.; Ali, M.; Saied, A.I.; Zakarya, M. Delta Calculus on Time Scale Formulas That Are Similar to Hilbert-Type Inequalities. Mathematics 2024, 12, 104.
Rezk, H.M.; Valdés, J.E.N.; Ali, M.; Saied, A.I.; Zakarya, M. Delta Calculus on Time Scale Formulas That Are Similar to Hilbert-Type Inequalities. Mathematics2024, 12, 104.
Rezk, H.M.; Valdés, J.E.N.; Ali, M.; Saied, A.I.; Zakarya, M. Delta Calculus on Time Scale Formulas That Are Similar to Hilbert-Type Inequalities. Mathematics 2024, 12, 104.
Abstract
In this article, we establish some new generalized inequalities of Hilbert-type on time scales delta calculus which considered as similar formulas for inequalities of Hilbert type proved by Chang-Jian, Lian-Ying and Cheung [7]. These inequalities will proved by applying Hölder’s inequality, chain rule on time scales and the mean inequality. As special cases of our results (when T = N and T = R), we get the discrete and continuous inequalities. Also, we can obtain other inequalities in different time scale, like T = q^Z, q > 1.
Keywords
Hilbert-type inequalities, Hölder’s inequality, Mean inequality, kernels, delta integrals, 7 time scales
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
