scholarly journals On Some Generalized Simpson’s and Newton’s Inequalities for (α, m)-Convex Functions in q-Calculus

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3266
Author(s):  
Ifra Bashir Sial ◽  
Sun Mei ◽  
Muhammad Aamir Ali ◽  
Kamsing Nonlaopon
Keyword(s):  
Convex Functions ◽  
Quantum Integral

In this paper, we first establish two right-quantum integral equalities involving a right-quantum derivative and a parameter m∈ 0,1. Then, we prove modified versions of Simpson’s and Newton’s type inequalities using established equalities for right-quantum differentiable α,m-convex functions. The newly developed inequalities are also proven to be expansions of comparable inequalities found in the literature.

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 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 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 Quantum Integral Inequalities with Respect to Raina’s Function via Coordinated Generalized Ψ -Convex Functions with Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Saima Rashid ◽  
Saad Ihsan Butt ◽  
Shazia Kanwal ◽  
Hijaz Ahmad ◽  
Miao-Kun Wang
Keyword(s):  
Quantum Theory ◽  
Real World ◽  
Convex Functions ◽  
Integral Identity ◽  
Special Functions ◽  
Type Inequality ◽  
The Novel ◽  
Quantum Calculus ◽  
Quantum Integral ◽  
Formula Type

In accordance with the quantum calculus, we introduced the two variable forms of Hermite-Hadamard- ( H H -) type inequality over finite rectangles for generalized Ψ -convex functions. This novel framework is the convolution of quantum calculus, convexity, and special functions. Taking into account the q ^ 1 q ^ 2 -integral identity, we demonstrate the novel generalizations of the H H -type inequality for q ^ 1 q ^ 2 -differentiable function by acquainting Raina’s functions. Additionally, we present a different approach that can be used to characterize H H -type variants with respect to Raina’s function of coordinated generalized Ψ -convex functions within the quantum techniques. This new study has the ability to generate certain novel bounds and some well-known consequences in the relative literature. As application viewpoint, the proposed study for changing parametric values associated with Raina’s functions exhibits interesting results in order to show the applicability and supremacy of the obtained results. It is expected that this method which is very useful, accurate, and versatile will open a new venue for the real-world phenomena of special relativity and quantum theory.

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 Erratum: Simpson type quantum integral inequalities for convex functions

2021 ◽  
Vol 22 (1) ◽  
pp. 33
Author(s):  
Necmettin Alp
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
Quantum Integral

scholarly journals Some new Hermite-Hadamard type inequalities for h-convex functions via quantum integral on finite intervals

2018 ◽  
Vol 18 (01) ◽  
pp. 74-86
Author(s):  
Limin Yang ◽  
Ruiyun Yang
Keyword(s):  
Convex Functions ◽  
Quantum Integral
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