Some new hermite–hadamard and related inequalities for convex functions via (P, q)-integral

Miguel Vivas-Cortez; Muhammad Aamir Ali; Hüseyin Budak; Humaira Kalsoom; Praveen Agarwal

doi:10.3390/e23070828

Some new hermite–hadamard and related inequalities for convex functions via (P, q)-integral

Miguel Vivas-Cortez
, Muhammad Aamir Ali^*
, Hüseyin Budak
, Humaira Kalsoom^*
, Praveen Agarwal

^*Corresponding author for this work

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

54 Scopus citations

Abstract

In this investigation, for convex functions, some new (p, q)–Hermite–Hadamard-type inequalities using the notions of (p, q)^π2 derivative and (p, q)^π2 integral are obtained. Furthermore, for (p, q)^π2-differentiable convex functions, some new (p, q) estimates for midpoint and trapezoidal-type inequalities using the notions of (p, q)^π2 integral are offered. It is also shown that the newly proved results for p = 1 and q → 1⁻ can be converted into some existing results. Finally, we discuss how the special means can be used to address newly discovered inequalities.

Original language	English
Article number	828
Journal	Entropy
Volume	23
Issue number	7
DOIs	https://doi.org/10.3390/e23070828
State	Published - Jul 2021
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2021 by the authors. Licensee MDPI, Basel, Switzerland.

Funding

Funding: This work is partially supported by National Natural Sciences Foundation of China (Grant No. 11971241). This work is partially supported by National Natural Sciences Foundation of China (Grant No. 11971241).The Chinese government is acknowledged for providing full scholarship for Ph.D. studies to Muhammad Aamir Ali. We want to give thanks to the Direcci?n de investigaci?n from Pontificia Universidad Cat?lica del Ecuador for technical support to our research project entitled: ?Algunas desigualdades integrales para funciones convexas generalizadas y aplicaciones?.

Funders	Funder number
Pontificia Universidad Católica del Ecuador
National Natural Science Foundation of China	11971241

Keywords

(p, q) estimates for midpoint and trapezoidal type inequalities
Post-quantum calculus
Quantum calculus

Access to Document

10.3390/e23070828

Cite this

@article{068ed116705c4a74a25c1ff7f354944f,

title = "Some new hermite–hadamard and related inequalities for convex functions via (P, q)-integral",

abstract = "In this investigation, for convex functions, some new (p, q)–Hermite–Hadamard-type inequalities using the notions of (p, q)π2 derivative and (p, q)π2 integral are obtained. Furthermore, for (p, q)π2-differentiable convex functions, some new (p, q) estimates for midpoint and trapezoidal-type inequalities using the notions of (p, q)π2 integral are offered. It is also shown that the newly proved results for p = 1 and q → 1− can be converted into some existing results. Finally, we discuss how the special means can be used to address newly discovered inequalities.",

keywords = "(p, q) estimates for midpoint and trapezoidal type inequalities, Post-quantum calculus, Quantum calculus",

author = "Miguel Vivas-Cortez and Ali, \{Muhammad Aamir\} and H{\"u}seyin Budak and Humaira Kalsoom and Praveen Agarwal",

note = "Publisher Copyright: {\textcopyright} 2021 by the authors. Licensee MDPI, Basel, Switzerland.",

year = "2021",

month = jul,

doi = "10.3390/e23070828",

language = "English",

volume = "23",

journal = "Entropy",

issn = "1099-4300",

publisher = "Multidisciplinary Digital Publishing Institute (MDPI)",

number = "7",

}

TY - JOUR

T1 - Some new hermite–hadamard and related inequalities for convex functions via (P, q)-integral

AU - Vivas-Cortez, Miguel

AU - Ali, Muhammad Aamir

AU - Budak, Hüseyin

AU - Kalsoom, Humaira

AU - Agarwal, Praveen

PY - 2021/7

Y1 - 2021/7

N2 - In this investigation, for convex functions, some new (p, q)–Hermite–Hadamard-type inequalities using the notions of (p, q)π2 derivative and (p, q)π2 integral are obtained. Furthermore, for (p, q)π2-differentiable convex functions, some new (p, q) estimates for midpoint and trapezoidal-type inequalities using the notions of (p, q)π2 integral are offered. It is also shown that the newly proved results for p = 1 and q → 1− can be converted into some existing results. Finally, we discuss how the special means can be used to address newly discovered inequalities.

AB - In this investigation, for convex functions, some new (p, q)–Hermite–Hadamard-type inequalities using the notions of (p, q)π2 derivative and (p, q)π2 integral are obtained. Furthermore, for (p, q)π2-differentiable convex functions, some new (p, q) estimates for midpoint and trapezoidal-type inequalities using the notions of (p, q)π2 integral are offered. It is also shown that the newly proved results for p = 1 and q → 1− can be converted into some existing results. Finally, we discuss how the special means can be used to address newly discovered inequalities.

KW - (p, q) estimates for midpoint and trapezoidal type inequalities

KW - Post-quantum calculus

KW - Quantum calculus

UR - https://www.scopus.com/pages/publications/85109392528

U2 - 10.3390/e23070828

DO - 10.3390/e23070828

M3 - Article

AN - SCOPUS:85109392528

SN - 1099-4300

VL - 23

JO - Entropy

JF - Entropy

IS - 7

M1 - 828

ER -

Some new hermite–hadamard and related inequalities for convex functions via (P, q)-integral

Abstract

Bibliographical note

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this