期刊
ADVANCES IN DIFFERENCE EQUATIONS
卷 2020, 期 1, 页码 -出版社
SPRINGER
DOI: 10.1186/s13662-020-02977-3
关键词
Hermite-Hadamard; m-polynomial convex; Interval-valued function; rho-Riemann-Liouville; 26D15; 26E25; 28B20
资金
- Natural Science Foundation of China [61673169, 11301127, 11701176, 11626101, 11601485]
The notion of m-polynomial convex interval-valued function Psi=[psi-,psi+] is hereby proposed. We point out a relationship that exists between Psi and its component real-valued functions psi- and psi+. For this class of functions, we establish loads of new set inclusions of the Hermite-Hadamard type involving the rho -Riemann-Liouville fractional integral operators. In particular, we prove, among other things, that if a set-valued function Psi defined on a convex set S is m-polynomial convex, rho ,E>0 and zeta,eta is an element of S, then mm+2-m-1Psi(zeta+eta 2)superset of Gamma rho (E+rho)(eta-zeta)E rho[rho J zeta +EPsi(eta)+rho J eta -EPsi(zeta)]superset of Psi(zeta)+Psi(eta )mSigma p=1mSp(E;rho), where Psi is Lebesgue integrable on [zeta,eta], Sp(E;rho)=2-EE+rho p-E rhoB(E rho,p+1) and B is the beta function. We extend, generalize, and complement existing results in the literature. By taking m >= 2, we derive loads of new and interesting inclusions. We hope that the idea and results obtained herein will be a catalyst towards further investigation.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据