Generalized fractal Jensen and Jensen–Mercer inequalities for harmonic convex function with applications

Saad Ihsan Butt; Praveen Agarwal; Saba Yousaf; Juan L.G. Guirao

doi:10.1186/s13660-021-02735-3

Generalized fractal Jensen and Jensen–Mercer inequalities for harmonic convex function with applications

Saad Ihsan Butt
, Praveen Agarwal
, Saba Yousaf
, Juan L.G. Guirao

Nonlinear Dynamic Research Centre (NDRC)

COMSATS University Islamabad
International College of Engineering
Technical University of Cartagena
Faculty of Sciences, King Abdulaziz University

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

49 Scopus citations

Abstract

In this paper, we present a generalized Jensen-type inequality for generalized harmonically convex function on the fractal sets, and a generalized Jensen–Mercer inequality involving local fractional integrals is obtained. Moreover, we establish some generalized Jensen–Mercer-type local fractional integral inequalities for harmonically convex function. Also, we obtain some generalized related results using these inequalities on the fractal space. Finally, we give applications of generalized means and probability density function.

Original language	English
Article number	1
Journal	Journal of Inequalities and Applications
Volume	2022
Issue number	1
DOIs	https://doi.org/10.1186/s13660-021-02735-3
State	Published - 2022

Keywords

Fractal space
Generalized harmonic convex function
Harmonic convex function
Jensen-type inequality
Jensen–Mercer inequality
Local fractional derivative
Local fractional integral

Access to Document

10.1186/s13660-021-02735-3

Cite this

@article{1a323e87f29948109bd1b28ffb2df5c3,

title = "Generalized fractal Jensen and Jensen–Mercer inequalities for harmonic convex function with applications",

abstract = "In this paper, we present a generalized Jensen-type inequality for generalized harmonically convex function on the fractal sets, and a generalized Jensen–Mercer inequality involving local fractional integrals is obtained. Moreover, we establish some generalized Jensen–Mercer-type local fractional integral inequalities for harmonically convex function. Also, we obtain some generalized related results using these inequalities on the fractal space. Finally, we give applications of generalized means and probability density function.",

keywords = "Fractal space, Generalized harmonic convex function, Harmonic convex function, Jensen-type inequality, Jensen–Mercer inequality, Local fractional derivative, Local fractional integral",

author = "Butt, \{Saad Ihsan\} and Praveen Agarwal and Saba Yousaf and Guirao, \{Juan L.G.\}",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s).",

year = "2022",

doi = "10.1186/s13660-021-02735-3",

language = "English",

volume = "2022",

journal = "Journal of Inequalities and Applications",

issn = "1025-5834",

publisher = "Springer Nature",

number = "1",

}

TY - JOUR

T1 - Generalized fractal Jensen and Jensen–Mercer inequalities for harmonic convex function with applications

AU - Butt, Saad Ihsan

AU - Agarwal, Praveen

AU - Yousaf, Saba

AU - Guirao, Juan L.G.

PY - 2022

Y1 - 2022

N2 - In this paper, we present a generalized Jensen-type inequality for generalized harmonically convex function on the fractal sets, and a generalized Jensen–Mercer inequality involving local fractional integrals is obtained. Moreover, we establish some generalized Jensen–Mercer-type local fractional integral inequalities for harmonically convex function. Also, we obtain some generalized related results using these inequalities on the fractal space. Finally, we give applications of generalized means and probability density function.

AB - In this paper, we present a generalized Jensen-type inequality for generalized harmonically convex function on the fractal sets, and a generalized Jensen–Mercer inequality involving local fractional integrals is obtained. Moreover, we establish some generalized Jensen–Mercer-type local fractional integral inequalities for harmonically convex function. Also, we obtain some generalized related results using these inequalities on the fractal space. Finally, we give applications of generalized means and probability density function.

KW - Fractal space

KW - Generalized harmonic convex function

KW - Harmonic convex function

KW - Jensen-type inequality

KW - Jensen–Mercer inequality

KW - Local fractional derivative

KW - Local fractional integral

UR - https://www.scopus.com/pages/publications/85122191673

U2 - 10.1186/s13660-021-02735-3

DO - 10.1186/s13660-021-02735-3

M3 - Article

AN - SCOPUS:85122191673

SN - 1025-5834

VL - 2022

JO - Journal of Inequalities and Applications

JF - Journal of Inequalities and Applications

IS - 1

M1 - 1

ER -

Generalized fractal Jensen and Jensen–Mercer inequalities for harmonic convex function with applications

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this