Hermite–Hadamard type inequalities for co-ordinated convex and qausi-convex functions and their applications

• Published in: Journal of inequalities and applications Vol. 2019; no. 1; pp. 1 - 33
• Main Authors: Latif, Muhammad Amer, Rashid, Saima, Dragomir, Silvestru Sever, Chu, Yu-Ming
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 19.12.2019; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Applications of Mathematics; Co-ordinated convex function; Co-ordinated quasi-convex function; Continuity (mathematics); Convex analysis; Hermite–Hadamard inequality; Hölder integral inequality; Independent variables; Inequalities; Mathematics; Mathematics and Statistics; Moment of random variable; Random variables; Recent Advances in General Inequalities on Pure & Applied Mathematics and Related Areas; Co-ordinated convex function; 26D20; Co-ordinated quasi-convex function; Hermite–Hadamard inequality; Hölder integral inequality; Moment of random variable; 26D07; 26D15
• ISSN: 1029-242X; 1025-5834; 1029-242X
• DOI: 10.1186/s13660-019-2272-7

In the article, we present several Hermite–Hadamard type inequalities for the co-ordinated convex and quasi-convex functions and give an application to the product of the moment of two continuous and independent random variables. Our results are generalizations of some earlier results. Additionally, an illustrative example on the probability distribution is given to support our results.