A Refinement of Grüss Inequality via Cauchy-Schwarz’s Inequality for Discrete Random Variables

Authors

Nicuşor Minculete, Transilvania University of Braşov, 50 Iuliu Maniu, 500091, Braşov, RomˆaniaFollow
Augusta Rațiu, Faculty of Mathematics and Computer Science, Babes¸-Bolyai University, 1 Mihail Kog˘alniceanu, 400084 Cluj-Napoca, RomˆaniaFollow
Josip Pečarić, Faculty of Textile Technology, University of Zagreb, Pierottijeva 6, 10000 Zagreb, CroatiaFollow

Author Country (or Countries)

Romˆania

Abstract

If X and Y are discrete random variables in finite case, then using the inequality of Cauchy-Schwarz, we will obtain another inequality expressed by the variance and covariance. The aim of this paper is to obtain a new refinement of discrete version of Gr¨uss inequality. In the final we show that we can structure the set of random variables with equal probabilities as a Hilbert space and as a seminormed vector space.

Digital Object Identifier (DOI)

http://dx.doi.org/10.12785/amis/090106

Recommended Citation

Minculete, Nicuşor; Rațiu, Augusta; and Pečarić, Josip (2023) "A Refinement of Grüss Inequality via Cauchy-Schwarz’s Inequality for Discrete Random Variables," Applied Mathematics & Information Sciences: Vol. 09: Iss. 1, Article 13.
DOI: http://dx.doi.org/10.12785/amis/090106
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss1/13