Generalized (p, q)-analogues of Dragomir-Agarwal’s inequalities involving Raina’s function and applications

Miguel Vivas-Cortez; Muhammad Zakria Javed; Muhammad Uzair Awan; Artion Kashuri; Muhammad Aslam Noor

doi:10.3934/math.2022639

Generalized (p, q)-analogues of Dragomir-Agarwal’s inequalities involving Raina’s function and applications

Miguel Vivas-Cortez
, Muhammad Zakria Javed
, Muhammad Uzair Awan^*
, Artion Kashuri
, Muhammad Aslam Noor

^*Corresponding author for this work

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

2 Scopus citations

Abstract

In this paper, we introduce the class of generalized strongly convex functions using Raina’s function. We derive two new general auxiliary results involving first and second order (p, q)-differentiable functions and Raina’s function. Essentially using these identities and the generalized strongly convexity property of the functions, we also found corresponding new generalized post-quantum analogues of Dragomir-Agarwal’s inequalities. We discuss some special cases about generalized convex functions. To support our main results, we offer applications to special means, to hypergeometric functions, to Mittag-Leffler functions and also to (p, q)-differentiable functions of first and second order that are bounded in absolute value.

Original language	English
Pages (from-to)	11464-11486
Number of pages	23
Journal	AIMS Mathematics
Volume	7
Issue number	6
DOIs	https://doi.org/10.3934/math.2022639
State	Published - 13 Apr 2022

Bibliographical note

Publisher Copyright:
© 2022 the Author(s), licensee AIMS Press.

Funding

The authors would like to thank the editor and the anonymous reviewers for their valuable comments and suggestions. This research was funded by Dirección de Investigación from Pontificia Universidad Católica del Ecuador in the research project entitled “Some integrals inequalities and generalized convexity” (Algunas desigualdades integrales para funciones con algún tipo de convexidad generalizada y aplicaciones). The authors would like to thank the editor and the anonymous reviewers for their valuable comments and suggestions. This research was funded by Direcci?n de Investigaci?n from Pontificia Universidad Cat?lica del Ecuador in the research project entitled ?Some integrals inequalities and generalized convexity? (Algunas desigualdades integrales para funciones con alg?n tipo de convexidad generalizada y aplicaciones).

Funders
Pontificia Universidad Católica del Ecuador

Keywords

Dragomir-Agarwal’s inequality
Hölder inequality
Raina’s function
generalized strongly convex functions
post-quantum calculus
power-mean inequality

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10.3934/math.2022639

Cite this

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title = "Generalized (p, q)-analogues of Dragomir-Agarwal{\textquoteright}s inequalities involving Raina{\textquoteright}s function and applications",

abstract = "In this paper, we introduce the class of generalized strongly convex functions using Raina{\textquoteright}s function. We derive two new general auxiliary results involving first and second order (p, q)-differentiable functions and Raina{\textquoteright}s function. Essentially using these identities and the generalized strongly convexity property of the functions, we also found corresponding new generalized post-quantum analogues of Dragomir-Agarwal{\textquoteright}s inequalities. We discuss some special cases about generalized convex functions. To support our main results, we offer applications to special means, to hypergeometric functions, to Mittag-Leffler functions and also to (p, q)-differentiable functions of first and second order that are bounded in absolute value.",

keywords = "Dragomir-Agarwal{\textquoteright}s inequality, H{\"o}lder inequality, Raina{\textquoteright}s function, generalized strongly convex functions, post-quantum calculus, power-mean inequality",

author = "Miguel Vivas-Cortez and Javed, \{Muhammad Zakria\} and Awan, \{Muhammad Uzair\} and Artion Kashuri and Noor, \{Muhammad Aslam\}",

note = "Publisher Copyright: {\textcopyright} 2022 the Author(s), licensee AIMS Press.",

year = "2022",

month = apr,

day = "13",

doi = "10.3934/math.2022639",

language = "English",

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T1 - Generalized (p, q)-analogues of Dragomir-Agarwal’s inequalities involving Raina’s function and applications

AU - Vivas-Cortez, Miguel

AU - Javed, Muhammad Zakria

AU - Awan, Muhammad Uzair

AU - Kashuri, Artion

AU - Noor, Muhammad Aslam

PY - 2022/4/13

Y1 - 2022/4/13

N2 - In this paper, we introduce the class of generalized strongly convex functions using Raina’s function. We derive two new general auxiliary results involving first and second order (p, q)-differentiable functions and Raina’s function. Essentially using these identities and the generalized strongly convexity property of the functions, we also found corresponding new generalized post-quantum analogues of Dragomir-Agarwal’s inequalities. We discuss some special cases about generalized convex functions. To support our main results, we offer applications to special means, to hypergeometric functions, to Mittag-Leffler functions and also to (p, q)-differentiable functions of first and second order that are bounded in absolute value.

AB - In this paper, we introduce the class of generalized strongly convex functions using Raina’s function. We derive two new general auxiliary results involving first and second order (p, q)-differentiable functions and Raina’s function. Essentially using these identities and the generalized strongly convexity property of the functions, we also found corresponding new generalized post-quantum analogues of Dragomir-Agarwal’s inequalities. We discuss some special cases about generalized convex functions. To support our main results, we offer applications to special means, to hypergeometric functions, to Mittag-Leffler functions and also to (p, q)-differentiable functions of first and second order that are bounded in absolute value.

KW - Dragomir-Agarwal’s inequality

KW - Hölder inequality

KW - Raina’s function

KW - generalized strongly convex functions

KW - post-quantum calculus

KW - power-mean inequality

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Generalized (p, q)-analogues of Dragomir-Agarwal’s inequalities involving Raina’s function and applications

Abstract

Bibliographical note

Funding

Keywords

Access to Document

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