Post-Quantum Midpoint-Type Inequalities Associated with Twice-Differentiable Functions

Thanin Sitthiwirattham; Ghulam Murtaza; Muhammad Aamir Ali; Chanon Promsakon; Ifra Bashir Sial; Praveen Agarwal

doi:10.3390/axioms11020046

Post-Quantum Midpoint-Type Inequalities Associated with Twice-Differentiable Functions

Thanin Sitthiwirattham
, Ghulam Murtaza
, Muhammad Aamir Ali
, Chanon Promsakon
, Ifra Bashir Sial
, Praveen Agarwal

Suan Dusit Rajabhat University
University of Management and Technology
Nanjing Normal University
King Mongkut's University of Technology North Bangkok
Jiangsu University
International College of Engineering

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

5 Scopus citations

Abstract

In this study, first we establish a (p, q)-integral identity involving the second (p, q)-derivative, and then, we use this result to prove some new midpoint-type inequalities for twice-(p, q)-differentiable convex functions. It is also shown that the newly established results are the refinements of the comparable results in the literature.

Original language	English
Article number	46
Journal	Axioms
Volume	11
Issue number	2
DOIs	https://doi.org/10.3390/axioms11020046
State	Published - Feb 2022
Externally published	Yes

Keywords

(p, q)-calculus
Convex functions
Hermite–Hadamard inequality

Access to Document

10.3390/axioms11020046

Cite this

@article{b77881d191364727bfe802317d0a99d7,

title = "Post-Quantum Midpoint-Type Inequalities Associated with Twice-Differentiable Functions",

abstract = "In this study, first we establish a (p, q)-integral identity involving the second (p, q)-derivative, and then, we use this result to prove some new midpoint-type inequalities for twice-(p, q)-differentiable convex functions. It is also shown that the newly established results are the refinements of the comparable results in the literature.",

keywords = "(p, q)-calculus, Convex functions, Hermite–Hadamard inequality",

author = "Thanin Sitthiwirattham and Ghulam Murtaza and Ali, \{Muhammad Aamir\} and Chanon Promsakon and Sial, \{Ifra Bashir\} and Praveen Agarwal",

note = "Publisher Copyright: {\textcopyright} 2022 by the authors. Licensee MDPI, Basel, Switzerland.",

year = "2022",

month = feb,

doi = "10.3390/axioms11020046",

language = "English",

volume = "11",

journal = "Axioms",

issn = "2075-1680",

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

number = "2",

}

TY - JOUR

T1 - Post-Quantum Midpoint-Type Inequalities Associated with Twice-Differentiable Functions

AU - Sitthiwirattham, Thanin

AU - Murtaza, Ghulam

AU - Ali, Muhammad Aamir

AU - Promsakon, Chanon

AU - Sial, Ifra Bashir

AU - Agarwal, Praveen

PY - 2022/2

Y1 - 2022/2

N2 - In this study, first we establish a (p, q)-integral identity involving the second (p, q)-derivative, and then, we use this result to prove some new midpoint-type inequalities for twice-(p, q)-differentiable convex functions. It is also shown that the newly established results are the refinements of the comparable results in the literature.

AB - In this study, first we establish a (p, q)-integral identity involving the second (p, q)-derivative, and then, we use this result to prove some new midpoint-type inequalities for twice-(p, q)-differentiable convex functions. It is also shown that the newly established results are the refinements of the comparable results in the literature.

KW - (p, q)-calculus

KW - Convex functions

KW - Hermite–Hadamard inequality

UR - https://www.scopus.com/pages/publications/85123413160

U2 - 10.3390/axioms11020046

DO - 10.3390/axioms11020046

M3 - Article

AN - SCOPUS:85123413160

SN - 2075-1680

VL - 11

JO - Axioms

JF - Axioms

IS - 2

M1 - 46

ER -

Post-Quantum Midpoint-Type Inequalities Associated with Twice-Differentiable Functions

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this