Hermite-Hadamard-type inequalities for generalized trigonometrically and hyperbolic ρ-convex functions in two dimension

被引：0
|
作者：
Dragomir, Silvestru Sever [2 ,3 ]
Jleli, Mohamed [1 ]
Samet, Bessem [1 ]
机构：
[1] King Saud Univ, Coll Sci, Dept Math, POB 2455, Riyadh 11451, Saudi Arabia
[2] Victoria Univ, Math Coll Engn & Sci, POB 14428, Melbourne, Vic 8001, Australia
[3] Univ Witwatersrand, Sch Comp Sci & Appl Math, Private Bag 3, ZA-2050 Johannesburg, South Africa
来源：
OPEN MATHEMATICS | 2024年 / 22卷 / 01期
关键词：
Hermite-Hadamard-type inequalities; trigonometrically rho-convex functions; hyperbolic rho-convex functions; Bessel functions;
D O I：
10.1515/math-2024-0028
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this article, we establish Hermite-Hadamard-type inequalities for the two classes of functions X-+/-lambda (Omega) = {f is an element of C-2(Omega) : Delta f +/- lambda f >= 0}, where lambda > 0 and Omega is an open subset of R-2. We also obtain a characterization of the set X-lambda (Omega). Notice that in the one-dimensional case, if Omega = I (an open interval of R) and lambda = rho(2), rho > 0, then X-lambda (Omega) reduces to the class of functions f is an element of C-2 (I) such that f is trigonometrically rho-convex (resp. hyperbolic rho-convex) on I.
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页数：13
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