Hermite–Hadamard Type Inequalities Involving (k-p) Fractional Operator for Various Types of Convex Functions

Vuk Stojiljković; Rajagopalan Ramaswamy; Fahad Alshammari; Ola A. Ashour; Mohammed Lahy Hassan Alghazwani; Stojan Radenović

doi:10.3390/fractalfract6070376

Hermite–Hadamard Type Inequalities Involving (k-p) Fractional Operator for Various Types of Convex Functions

Vuk Stojiljković
, Rajagopalan Ramaswamy
, Fahad Alshammari
, Ola A. Ashour
, Mohammed Lahy Hassan Alghazwani
, Stojan Radenović

Mathematics

University of Novi Sad
Prince Sattam Bin Abdulaziz University
University of Belgrade

Research output: Contribution to journal › Article › peer-review

36 Scopus citations

Abstract

We establish various fractional convex inequalities of the Hermite–Hadamard type with addition to many other inequalities. Various types of such inequalities are obtained, such as (p, h) fractional type inequality and many others, as the (p, h)-convexity is the generalization of the other convex inequalities. As a consequence of the (h, m)-convexity, the fractional inequality of the (s, m)-type is obtained. Many consequences of such fractional inequalities and generalizations are obtained.

Original language	English
Article number	376
Journal	Fractal and Fractional
Volume	6
Issue number	7
DOIs	https://doi.org/10.3390/fractalfract6070376
State	Published - Jul 2022

Keywords

(h,m)-convex function
(p,h)-convex function
fractional inequality
Hermite–Hadamard inequality
Hölder inequality

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10.3390/fractalfract6070376

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title = "Hermite–Hadamard Type Inequalities Involving (k-p) Fractional Operator for Various Types of Convex Functions",

abstract = "We establish various fractional convex inequalities of the Hermite–Hadamard type with addition to many other inequalities. Various types of such inequalities are obtained, such as (p, h) fractional type inequality and many others, as the (p, h)-convexity is the generalization of the other convex inequalities. As a consequence of the (h, m)-convexity, the fractional inequality of the (s, m)-type is obtained. Many consequences of such fractional inequalities and generalizations are obtained.",

keywords = "(h,m)-convex function, (p,h)-convex function, fractional inequality, Hermite–Hadamard inequality, H{\"o}lder inequality",

author = "Vuk Stojiljkovi{\'c} and Rajagopalan Ramaswamy and Fahad Alshammari and Ashour, \{Ola A.\} and Alghazwani, \{Mohammed Lahy Hassan\} and Stojan Radenovi{\'c}",

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year = "2022",

month = jul,

doi = "10.3390/fractalfract6070376",

language = "English",

volume = "6",

journal = "Fractal and Fractional",

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T1 - Hermite–Hadamard Type Inequalities Involving (k-p) Fractional Operator for Various Types of Convex Functions

AU - Stojiljković, Vuk

AU - Ramaswamy, Rajagopalan

AU - Alshammari, Fahad

AU - Ashour, Ola A.

AU - Alghazwani, Mohammed Lahy Hassan

AU - Radenović, Stojan

PY - 2022/7

Y1 - 2022/7

N2 - We establish various fractional convex inequalities of the Hermite–Hadamard type with addition to many other inequalities. Various types of such inequalities are obtained, such as (p, h) fractional type inequality and many others, as the (p, h)-convexity is the generalization of the other convex inequalities. As a consequence of the (h, m)-convexity, the fractional inequality of the (s, m)-type is obtained. Many consequences of such fractional inequalities and generalizations are obtained.

AB - We establish various fractional convex inequalities of the Hermite–Hadamard type with addition to many other inequalities. Various types of such inequalities are obtained, such as (p, h) fractional type inequality and many others, as the (p, h)-convexity is the generalization of the other convex inequalities. As a consequence of the (h, m)-convexity, the fractional inequality of the (s, m)-type is obtained. Many consequences of such fractional inequalities and generalizations are obtained.

KW - (h,m)-convex function

KW - (p,h)-convex function

KW - fractional inequality

KW - Hermite–Hadamard inequality

KW - Hölder inequality

UR - https://www.scopus.com/pages/publications/85133604977

U2 - 10.3390/fractalfract6070376

DO - 10.3390/fractalfract6070376

M3 - Article

AN - SCOPUS:85133604977

SN - 2504-3110

VL - 6

JO - Fractal and Fractional

JF - Fractal and Fractional

IS - 7

M1 - 376

ER -

Hermite–Hadamard Type Inequalities Involving (k-p) Fractional Operator for Various Types of Convex Functions

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Keywords

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