Abstract
This paper deals with the derivation of some new dynamic Hilbert-type inequalities in time scale nabla calculus. In proving the results, the basic idea is to use some algebraic inequalities, Hölder’s inequality, and Jensen’s time scale inequality. This generalization allows us not only to unify all the related results that exist in the literature on an arbitrary time scale, but also to obtain new outcomes that are analytical to the results of the delta time scale calculation.
Highlights
In recent years, Hilbert’s dual-series inequality and its integral form [1, pp. 253–254] have been granted significant attention by many scholars
In [17] the researchers concluded some generalizations of inequalities (1) and (2) for time scale delta calculus
The main theorems are inspired from the paper [18] which presents the corresponding results for time scale delta calculus
Summary
Hilbert’s dual-series inequality and its integral form [1, pp. 253–254] have been granted significant attention by many scholars (for example, see [2,3,4,5,6,7,8,9,10]). Hilbert’s dual-series inequality and its integral form [1, pp. 253–254] have been granted significant attention by many scholars (for example, see [2,3,4,5,6,7,8,9,10]). G. Pachpatte [11] established a new inequality close to that of Hilbert as follows. In the same article [11], Pachpatte demonstrated the integral version of (1) as follows.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
