On generalizations of quantum Simpson’s and quantum newton’s inequalities with some parameters

Chanon Promsakon; Muhammad Aamir Ali; Hüseyin Budak; Mujahid Abbas; Faheem Muhammad; Thanin Sitthiwirattham

doi:10.3934/math.2021807

On generalizations of quantum Simpson’s and quantum newton’s inequalities with some parameters

Chanon Promsakon, Muhammad Aamir Ali, Hüseyin Budak, Mujahid Abbas, Faheem Muhammad, Thanin Sitthiwirattham

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

2 Citations (Scopus)

Abstract

In this paper, we prove two identities concerning quantum derivatives, quantum integrals, and some parameters. Using the newly proved identities, we prove new Simpson’s and Newton’s type inequalities for quantum differentiable convex functions with two and three parameters, respectively. We also look at the special cases of our key findings and find some new and old Simpson’s type inequalities, Newton’s type inequalities, midpoint type inequalities, and trapezoidal type inequalities.

Original language	English
Pages (from-to)	13954-13975
Number of pages	22
Journal	AIMS Mathematics
Volume	6
Issue number	12
DOIs	https://doi.org/10.3934/math.2021807
Publication status	Published - 2021
Externally published	Yes

Keywords

Convex functions
Newton’s inequalities
Quantum calculus
Simpson’s inequalities

ASJC Scopus subject areas

General Mathematics

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10.3934/math.2021807

Cite this

@article{79492547e26d4f4ab235a85f882dc67a,

title = "On generalizations of quantum Simpson{\textquoteright}s and quantum newton{\textquoteright}s inequalities with some parameters",

abstract = "In this paper, we prove two identities concerning quantum derivatives, quantum integrals, and some parameters. Using the newly proved identities, we prove new Simpson{\textquoteright}s and Newton{\textquoteright}s type inequalities for quantum differentiable convex functions with two and three parameters, respectively. We also look at the special cases of our key findings and find some new and old Simpson{\textquoteright}s type inequalities, Newton{\textquoteright}s type inequalities, midpoint type inequalities, and trapezoidal type inequalities.",

keywords = "Convex functions, Newton{\textquoteright}s inequalities, Quantum calculus, Simpson{\textquoteright}s inequalities",

author = "Chanon Promsakon and Ali, \{Muhammad Aamir\} and H{\"u}seyin Budak and Mujahid Abbas and Faheem Muhammad and Thanin Sitthiwirattham",

note = "Publisher Copyright: {\textcopyright} 2021 the Author(s), licensee AIMS Press.",

year = "2021",

doi = "10.3934/math.2021807",

language = "English",

volume = "6",

pages = "13954--13975",

journal = "AIMS Mathematics",

issn = "2473-6988",

publisher = "American Institute of Mathematical Sciences",

number = "12",

}

TY - JOUR

T1 - On generalizations of quantum Simpson’s and quantum newton’s inequalities with some parameters

AU - Promsakon, Chanon

AU - Ali, Muhammad Aamir

AU - Budak, Hüseyin

AU - Abbas, Mujahid

AU - Muhammad, Faheem

AU - Sitthiwirattham, Thanin

PY - 2021

Y1 - 2021

N2 - In this paper, we prove two identities concerning quantum derivatives, quantum integrals, and some parameters. Using the newly proved identities, we prove new Simpson’s and Newton’s type inequalities for quantum differentiable convex functions with two and three parameters, respectively. We also look at the special cases of our key findings and find some new and old Simpson’s type inequalities, Newton’s type inequalities, midpoint type inequalities, and trapezoidal type inequalities.

AB - In this paper, we prove two identities concerning quantum derivatives, quantum integrals, and some parameters. Using the newly proved identities, we prove new Simpson’s and Newton’s type inequalities for quantum differentiable convex functions with two and three parameters, respectively. We also look at the special cases of our key findings and find some new and old Simpson’s type inequalities, Newton’s type inequalities, midpoint type inequalities, and trapezoidal type inequalities.

KW - Convex functions

KW - Newton’s inequalities

KW - Quantum calculus

KW - Simpson’s inequalities

UR - https://www.scopus.com/pages/publications/85115886015

U2 - 10.3934/math.2021807

DO - 10.3934/math.2021807

M3 - Article

AN - SCOPUS:85115886015

SN - 2473-6988

VL - 6

SP - 13954

EP - 13975

JO - AIMS Mathematics

JF - AIMS Mathematics

IS - 12

ER -

On generalizations of quantum Simpson’s and quantum newton’s inequalities with some parameters

Abstract

Keywords

ASJC Scopus subject areas

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