scholarly journals Some New Simpson’s and Newton’s Formulas Type Inequalities for Convex Functions in Quantum Calculus

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1992
Author(s):  
Pimchana Siricharuanun ◽  
Samet Erden ◽  
Muhammad Aamir Ali ◽  
Hüseyin Budak ◽  
Saowaluck Chasreechai ◽  
...  
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
Quantum Calculus ◽  
Quantum Integral ◽  
Classical Integral

In this paper, using the notions of qκ2-quantum integral and qκ2-quantum derivative, we present some new identities that enable us to obtain new quantum Simpson’s and quantum Newton’s type inequalities for quantum differentiable convex functions. This paper, in particular, generalizes and expands previous findings in the field of quantum and classical integral inequalities obtained by various authors.

scholarly journals Certain Generalized Quantum Simpson's and Quantum Newton's type Inequalities for Convex Functions in Quantum Calculus

2020 ◽  
Author(s):  
Muhammad Aamir Ali ◽  
Hüseyin BUDAK ◽  
PRAVEEN AGARWAL ◽  
Yuming Chu
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
Quantum Calculus ◽  
Quantum Integral ◽  
Classical Integral

In this paper first we present some new identities by using the notions of quantum integrals and derivatives which allows us to obtain new quantum Simpson’s and quantum Newton’s type inequalities for differentiable convex functions by using the q_{x}-quantum integral and q^{y}-quantum integral. In particular, this paper generalises and extends previous results obtained by the various authors in the field of quantum and classical integral inequalities.

scholarly journals A new generalization of some quantum integral inequalities for quantum differentiable convex functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yi-Xia Li ◽  
Muhammad Aamir Ali ◽  
Hüseyin Budak ◽  
Mujahid Abbas ◽  
Yu-Ming Chu
Keyword(s):  
Integral Inequality ◽  
Convex Functions ◽  
Integral Identity ◽  
Integral Inequalities ◽  
Quantum Integral ◽  
Special Cases

AbstractIn this paper, we offer a new quantum integral identity, the result is then used to obtain some new estimates of Hermite–Hadamard inequalities for quantum integrals. The results presented in this paper are generalizations of the comparable results in the literature on Hermite–Hadamard inequalities. Several inequalities, such as the midpoint-like integral inequality, the Simpson-like integral inequality, the averaged midpoint–trapezoid-like integral inequality, and the trapezoid-like integral inequality, are obtained as special cases of our main results.

scholarly journals Quantum Trapezium-Type Inequalities Using Generalized ϕ-Convex Functions

Axioms ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 12 ◽  
Author(s):  
Miguel J. Vivas-Cortez ◽  
Artion Kashuri ◽  
Rozana Liko ◽  
Jorge E. Hernández
Keyword(s):  
Hypergeometric Function ◽  
Convex Functions ◽  
Special Functions ◽  
Integral Inequalities ◽  
Quantum Calculation ◽  
Generalized Convex Functions ◽  
Hadamard Inequality ◽  
Trapezium Type ◽  
Quantum Integral

In this work, a study is conducted on the Hermite–Hadamard inequality using a class of generalized convex functions that involves a generalized and parametrized class of special functions within the framework of quantum calculation. Similar results can be obtained from the results found for functions such as the hypergeometric function and the classical Mittag–Leffler function. The method used to obtain the results is classic in the study of quantum integral inequalities.

scholarly journals Simpson type quantum integral inequalities for convex functions

2018 ◽  
Vol 19 (1) ◽  
pp. 649 ◽  
Author(s):  
M. Tunc ◽  
E. Göv ◽  
S. Balgecti
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
Quantum Integral

scholarly journals Quantum integral inequalities for convex functions

2015 ◽  
pp. 781-793 ◽  
Author(s):  
Weerawat Sudsutad ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
Quantum Integral

scholarly journals Some Inequalities Using Generalized Convex Functions in Quantum Analysis

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1402 ◽  
Author(s):  
Miguel J. Vivas-Cortez ◽  
Artion Kashuri ◽  
Rozana Liko ◽  
Jorge E. Hernández Hernández
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
Generalized Convex Functions ◽  
Hadamard Inequality ◽  
Quantum Calculus ◽  
Quantum Analysis ◽  
Real Functions ◽  
Definition Of

In the present work, the Hermite–Hadamard inequality is established in the setting of quantum calculus for a generalized class of convex functions depending on three parameters: a number in ( 0 , 1 ] and two arbitrary real functions defined on [ 0 , 1 ] . From the proven results, various inequalities of the same type are deduced for other types of generalized convex functions and the methodology used reveals, in a sense, a symmetric mathematical phenomenon. In addition, the definition of dominated convex functions with respect to the generalized class of convex functions aforementioned is introduced, and some integral inequalities are established.

scholarly journals Montgomery identity and Ostrowski-type inequalities via quantum calculus

2021 ◽  
Vol 19 (1) ◽  
pp. 1098-1109
Author(s):  
Thanin Sitthiwirattham ◽  
Muhammad Aamir Ali ◽  
Huseyin Budak ◽  
Mujahid Abbas ◽  
Saowaluck Chasreechai
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
Montgomery Identity ◽  
Quantum Calculus ◽  
Special Cases ◽  
Quantum Version

Abstract In this paper, we prove a quantum version of Montgomery identity and prove some new Ostrowski-type inequalities for convex functions in the setting of quantum calculus. Moreover, we discuss several special cases of newly established inequalities and obtain different new and existing inequalities in the field of integral inequalities.

scholarly journals Some New Newton’s Type Integral Inequalities for Co-Ordinated Convex Functions in Quantum Calculus

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1476 ◽  
Author(s):  
Miguel Vivas-Cortez ◽  
Muhammad Aamir Ali ◽  
Artion Kashuri ◽  
Ifra Bashir Sial ◽  
Zhiyue Zhang
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
Convexity Property ◽  
Integral Approximation ◽  
Quantum Calculus ◽  
Simpson’S Rule ◽  
Type Integral ◽  
Simpson's Rule ◽  
Ordinary Integral ◽  
New Inequalities

Some recent results have been found treating the famous Simpson’s rule in connection with the convexity property of functions and those called generalized convex. The purpose of this article is to address Newton-type integral inequalities by associating with them certain criteria of quantum calculus and the convexity of the functions of various variables. In this article, by using the concept of recently defined q1q2 -derivatives and integrals, some of Newton’s type inequalities for co-ordinated convex functions are revealed. We also employ the limits of q1,q2→1− in new results, and attain some new inequalities of Newton’s type for co-ordinated convex functions through ordinary integral. Finally, we provide a thorough application of the newly obtained key outcomes, these new consequences can be useful in the integral approximation study for symmetrical functions, or with some kind of symmetry.

scholarly journals Certain Fractional Proportional Integral Inequalities via Convex Functions

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 222 ◽  
Author(s):  
Gauhar Rahman ◽  
Kottakkaran Sooppy Nisar ◽  
Thabet Abdeljawad ◽  
Samee Ullah
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Fractional Integral Operators ◽  
Proportional Integral ◽  
Special Cases ◽  
Classical Integral

The goal of this article is to establish some fractional proportional integral inequalities for convex functions by employing proportional fractional integral operators. In addition, we establish some classical integral inequalities as the special cases of our main findings.

scholarly journals Hermite–Hadamard integral inequalities on coordinated convex functions in quantum calculus

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Manar A. Alqudah ◽  
Artion Kashuri ◽  
Pshtiwan Othman Mohammed ◽  
Thabet Abdeljawad ◽  
Muhammad Raees ◽  
...  
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
Quantum Calculus ◽  
Formula Type

AbstractAt first, we recall the q-operators in the context of q-calculus and by examining these operators we will introduce new definitions of the partial q-operators. Then, we investigate some new refinements inequalities of Hermite–Hadamard ($H-H$ H − H ) type on the coordinated convex functions involving the new defined partial q-operators. From our main results, we establish several specific inequalities and we point out the existing results which had already been obtained in the literature.

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