Abstract
We establish some new refinements to the Holder inequality. We then apply them to provide some refinements to the extended Euler’s gamma and beta functions. As another application of our results, we give a new proof of the equivalence between the Holder inequality and the Cauchy-Schwarz inequality.
Highlights
Let (Ω, F, μ) be a measure space (μ is a positive measure)
We provide a new proof of the equivalence between the Holder’s and Cauchy-Schwarz inequalities
We have given some new refinements to the Holder inequality
Summary
Let (Ω, F, μ) be a measure space (μ is a positive measure). For any mesurable functions f, g : Ω 7→ C on Ω, we recall the Holder’s inequality: Z μZ |f g|dμ ≤. There are many connections between classical discrete inequalities Some of these connections were noted in several chapters of the book [13], where in particular the equivalence (H)d ⇐⇒ (C.S)d was obtained after some intermidiate results. It is known, from the book [12] of A.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
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.
