On some inequalities for uniformly convex mapping with estimations to normal distributions

Autor:	Saad Ihsan Butt, Yamin Sayyari, Praveen Agarwal, Juan J. Nieto, Muhammad Umar
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	Hermite–Mercer inequality Uniformly convex functions Integral inequalities Fractional integrals Mathematics QA1-939
Zdroj:	Journal of Inequalities and Applications, Vol 2023, Iss 1, Pp 1-29 (2023)
Druh dokumentu:	article
ISSN:	1029-242X
DOI:	10.1186/s13660-023-02997-z
Popis:	Abstract In this paper, we introduce notable Jensen–Mercer inequality for a general class of convex functions, namely uniformly convex functions. We explore some interesting properties of such a class of functions along with some examples. As a result, we establish Hermite–Jensen–Mercer inequalities pertaining uniformly convex functions by considering the class of fractional integral operators. Moreover, we establish Mercer–Ostrowski inequalities for conformable integral operator via differentiable uniformly convex functions. Finally, we apply our inequalities to get estimations for normal probability distributions (Gaussian distributions).
Databáze:	Directory of Open Access Journals
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