Some New Hermite-Hadamard-Fejer Fractional Type Inequalities for h-Convex and Harmonically h-Convex Interval-Valued Functions

被引：27

作者：

Kalsoom, Humaira ^{[1
]}

Latif, Muhammad Amer ^{[2
]}

Khan, Zareen A. ^{[3
]}

Vivas-Cortez, Miguel ^{[4
]}

机构：

[1] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Zhejiang, Peoples R China

[2] King Faisal Univ, Dept Basic Sci, Al Hufuf 31982, Al Hasa, Saudi Arabia

[3] Princess Nourah Bint Abdulrahman Univ, Dept Math Sci, Coll Sci, POB 84428, Riyadh 11671, Saudi Arabia

[4] Pontificia Univ Catolica Ecuador, Fac Ciencias Nat & Exactas, Escuela Ciencias Fis & Matemat, Sede Quito 17012184, Ecuador

来源：

MATHEMATICS | 2022年 / 10卷 / 01期

关键词：

weighted interval-valued fractional operators; h-convex interval-valued functions; h-harmonically convex interval-valued functions; weighted interval-valued Hermite-Hadamard type inequality; VARIABLE-ORDER;

D O I：

10.3390/math10010074

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, firstly, we establish a novel definition of weighted interval-valued fractional integrals of a function Upsilon using an another function & thetasym;(zeta). As an additional observation, it is noted that the new class of weighted interval-valued fractional integrals of a function Upsilon by employing an additional function & thetasym;(zeta) characterizes a variety of new classes as special cases, which is a generalization of the previous class. Secondly, we prove a new version of the Hermite-Hadamard-Fejer type inequality for h-convex interval-valued functions using weighted interval-valued fractional integrals of a function Upsilon according to another function & thetasym;(zeta). Finally, by using weighted interval-valued fractional integrals of a function Upsilon according to another function & thetasym;(zeta), we are establishing a new Hermite-Hadamard-Fejer type inequality for harmonically h-convex interval-valued functions that is not previously known. Moreover, some examples are provided to demonstrate our results.

引用

页数：22