scholarly journals On Some New Simpson’s Formula Type Inequalities for Convex Functions in Post-Quantum Calculus

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2419
Author(s):  
Miguel J. Vivas-Cortez ◽  
Muhammad Aamir Ali ◽  
Shahid Qaisar ◽  
Ifra Bashir Sial ◽  
Sinchai Jansem ◽  
...  
Keyword(s):  
Convex Functions ◽  
Integral Identity ◽  
Quantum Calculus ◽  
Formula Type

In this work, we prove a new (p,q)-integral identity involving a (p,q)-derivative and (p,q)-integral. The newly established identity is then used to show some new Simpson’s formula type inequalities for (p,q)-differentiable convex functions. Finally, the newly discovered results are shown to be refinements of comparable results in the literature. Analytic inequalities of this type, as well as the techniques used to solve them, have applications in a variety of fields where symmetry is important.

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 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.

scholarly journals Quantum estimates in two variable forms for Simpson-type inequalities considering generalized Ψ-convex functions with applications

Open Physics ◽  
2021 ◽  
Vol 19 (1) ◽  
pp. 305-326
Author(s):  
Yu-Ming Chu ◽  
Asia Rauf ◽  
Saima Rashid ◽  
Safeera Batool ◽  
Y. S. Hamed
Keyword(s):  
Real World ◽  
Convex Functions ◽  
Integral Identity ◽  
Quantum Physics ◽  
Higher Order ◽  
New Approach ◽  
Quantum Calculus ◽  
Opening Up ◽  
Integral Identities

Abstract This article proposes a new approach based on quantum calculus framework employing novel classes of higher order strongly generalized Ψ \Psi -convex and quasi-convex functions. Certain pivotal inequalities of Simpson-type to estimate innovative variants under the q ˇ 1 , q ˇ 2 {\check{q}}_{1},{\check{q}}_{2} -integral and derivative scheme that provides a series of variants correlate with the special Raina’s functions. Meanwhile, a q ˇ 1 , q ˇ 2 {\check{q}}_{1},{\check{q}}_{2} -integral identity is presented, and new theorems with novel strategies are provided. As an application viewpoint, we tend to illustrate two-variable q ˇ 1 q ˇ 2 {\check{q}}_{1}{\check{q}}_{2} -integral identities and variants of Simpson-type in the sense of hypergeometric and Mittag–Leffler functions and prove the feasibility and relevance of the proposed approach. This approach is supposed to be reliable and versatile, opening up new avenues for the application of classical and quantum physics to real-world anomalies.

Some new generalizations for GA-convex functions

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 1009-1016 ◽  
Author(s):  
Ahmet Akdemir ◽  
Özdemir Emin ◽  
Ardıç Avcı ◽  
Abdullatif Yalçın
Keyword(s):  
Convex Functions ◽  
Integral Identity ◽  
Integral Inequalities ◽  
General Integral ◽  
Second Derivatives ◽  
Derivatives Of

In this paper, firstly we prove an integral identity that one can derive several new equalities for special selections of n from this identity: Secondly, we established more general integral inequalities for functions whose second derivatives of absolute values are GA-convex functions based on this equality.

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 Simpson type inequalities and applications

2021 ◽  
Author(s):  
Muhammad Uzair Awan ◽  
Muhammad Zakria Javed ◽  
Michael Th. Rassias ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor
Keyword(s):  
Quadrature Formula ◽  
Convex Functions ◽  
Integral Identity ◽  
Higher Order ◽  
Auxiliary Result ◽  
First Order ◽  
New Class ◽  
Differentiable Functions

AbstractA new generalized integral identity involving first order differentiable functions is obtained. Using this identity as an auxiliary result, we then obtain some new refinements of Simpson type inequalities using a new class called as strongly (s, m)-convex functions of higher order of $$\sigma >0$$ σ > 0 . We also discuss some interesting applications of the obtained results in the theory of means. In last we present applications of the obtained results in obtaining Simpson-like quadrature formula.

scholarly journals Better Approaches for n-Times Differentiable Convex Functions

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 950 ◽  
Author(s):  
Praveen Agarwal ◽  
Mahir Kadakal ◽  
İmdat İşcan ◽  
Yu-Ming Chu
Keyword(s):  
Convex Functions ◽  
Integral Identity ◽  
Special Means ◽  
New Inequalities

In this work, by using an integral identity together with the Hölder–İşcan inequality we establish several new inequalities for n-times differentiable convex and concave mappings. Furthermore, various applications for some special means as arithmetic, geometric, and logarithmic are given.

scholarly journals New Inequalities for Strongly r-Convex Functions

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Huriye Kadakal
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Integral Identity ◽  
Integral Inequalities ◽  
Special Cases ◽  
Class Of Functions ◽  
New Inequalities

In this study, firstly we introduce a new concept called “strongly r-convex function.” After that we establish Hermite-Hadamard-like inequalities for this class of functions. Moreover, by using an integral identity together with some well known integral inequalities, we establish several new inequalities for n-times differentiable strongly r-convex functions. In special cases, the results obtained coincide with the well-known results in the literature.

scholarly journals Some New Simpson’s-Formula-Type Inequalities for Twice-Differentiable Convex Functions via Generalized Fractional Operators

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2249
Author(s):  
Muhammad Aamir Ali ◽  
Hasan Kara ◽  
Jessada Tariboon ◽  
Suphawat Asawasamrit ◽  
Hüseyin Budak ◽  
...  
Keyword(s):  
Convex Functions ◽  
Fractional Operators ◽  
The Past ◽  
Differentiable Functions ◽  
Simpson’S Inequality ◽  
Special Cases ◽  
Wide Range ◽  
Generalized Fractional Integral ◽  
The Subject ◽  
Formula Type

From the past to the present, various works have been dedicated to Simpson’s inequality for differentiable convex functions. Simpson-type inequalities for twice-differentiable functions have been the subject of some research. In this paper, we establish a new generalized fractional integral identity involving twice-differentiable functions, then we use this result to prove some new Simpson’s-formula-type inequalities for twice-differentiable convex functions. Furthermore, we examine a few special cases of newly established inequalities and obtain several new and old Simpson’s-formula-type inequalities. These types of analytic inequalities, as well as the methodologies for solving them, have applications in a wide range of fields where symmetry is crucial.

scholarly journals Some new Caputo fractional derivative inequalities for exponentially $ (\theta, h-m) $–convex functions

2021 ◽  
Vol 7 (2) ◽  
pp. 3006-3026
Author(s):  
Imran Abbas Baloch ◽  
◽  
Thabet Abdeljawad ◽  
Sidra Bibi ◽  
Aiman Mukheimer ◽  
...  
Keyword(s):  
Fractional Derivative ◽  
Caputo Fractional Derivative ◽  
Convex Functions ◽  
Integral Identity ◽  
Fractional Derivatives ◽  
Order Derivative ◽  
Special Cases

<abstract><p>Firstly, we obtain some inequalities of Hadamard type for exponentially $ (\theta, h-m) $–convex functions via Caputo $ k $–fractional derivatives. Secondly, using integral identity including the $ (n+1) $–order derivative of a given function via Caputo $ k $-fractional derivatives we prove some of its related results. Some new results are given and known results are recaptured as special cases from our results.</p></abstract>

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