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 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.

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 Analogs of Ostrowski-Type Inequalities for Raina’s Function correlated with Coordinated Generalized Φ-Convex Functions

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 308 ◽  
Author(s):  
Hong-Hu Chu ◽  
Humaira Kalsoom ◽  
Saima Rashid ◽  
Muhammad Idrees ◽  
Farhat Safdar ◽  
...  
Keyword(s):  
Quantum Theory ◽  
Differentiable Function ◽  
Convex Functions ◽  
Numerical Scheme ◽  
Special Functions ◽  
Auxiliary Result ◽  
Quantum Calculus ◽  
New Directions ◽  
Quantum Approach ◽  
Quantum Behavior

In this paper, the newly proposed concept of Raina’s function and quantum calculus are utilized to anticipate the quantum behavior of two variable Ostrowski-type inequalities. This new technique is the convolution of special functions with hypergeometric and Mittag–Leffler functions, respectively. This new concept will have the option to reduce self-similitudes in the quantum attractors under investigation. We discuss the implications and other consequences of the quantum Ostrowski-type inequalities by deriving an auxiliary result for a q 1 q 2 -differentiable function by inserting Raina’s functions. Meanwhile, we present a numerical scheme that can be used to derive variants for Ostrowski-type inequalities in the sense of coordinated generalized Φ -convex functions with the quantum approach. This new scheme of study for varying values of parameters with the involvement of Raina’s function yields extremely intriguing outcomes with an illustrative example. It is supposed that this investigation will provide new directions for the capricious nature of quantum theory.

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 New Estimations of Hermite–Hadamard Type Integral Inequalities for Special Functions

2021 ◽  
Vol 5 (4) ◽  
pp. 144
Author(s):  
Hijaz Ahmad ◽  
Muhammad Tariq ◽  
Soubhagya Kumar Sahoo ◽  
Jamel Baili ◽  
Clemente Cesarano
Keyword(s):  
Special Functions ◽  
Type Inequality ◽  
Integral Inequalities ◽  
The Novel ◽  
Current Pattern ◽  
Hadamard Inequality ◽  
Special Means ◽  
Algebraic Properties ◽  
Type Integral ◽  
Generalized Integral Inequalities

In this paper, we propose some generalized integral inequalities of the Raina type depicting the Mittag–Leffler function. We introduce and explore the idea of generalized s-type convex function of Raina type. Based on this, we discuss its algebraic properties and establish the novel version of Hermite–Hadamard inequality. Furthermore, to improve our results, we explore two new equalities, and employing these we present some refinements of the Hermite–Hadamard-type inequality. A few remarkable cases are discussed, which can be seen as valuable applications. Applications of some of our presented results to special means are given as well. An endeavor is made to introduce an almost thorough rundown of references concerning the Mittag–Leffler functions and the Raina functions to make the readers acquainted with the current pattern of emerging research in various fields including Mittag–Leffler and Raina type functions. Results established in this paper can be viewed as a significant improvement of previously known results.

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 Some Parameterized Quantum Midpoint and Quantum Trapezoid Type Inequalities for Convex Functions with Applications

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 996
Author(s):  
Suphawat Asawasamrit ◽  
Muhammad Aamir Ali ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Information Theory ◽  
Convex Functions ◽  
Strong Association ◽  
Type Inequality ◽  
Quadrature Formulas ◽  
Quantum Calculus ◽  
Interdisciplinary Field ◽  
Integral Equality ◽  
Entropy Functions ◽  
Science Information

Quantum information theory, an interdisciplinary field that includes computer science, information theory, philosophy, cryptography, and entropy, has various applications for quantum calculus. Inequalities and entropy functions have a strong association with convex functions. In this study, we prove quantum midpoint type inequalities, quantum trapezoidal type inequalities, and the quantum Simpson’s type inequality for differentiable convex functions using a new parameterized q-integral equality. The newly formed inequalities are also proven to be generalizations of previously existing inequities. Finally, using the newly established inequalities, we present some applications for quadrature formulas.

scholarly journals Novel Refinements via n –Polynomial Harmonically s –Type Convex Functions and Application in Special Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Saad Ihsan Butt ◽  
Saima Rashid ◽  
Muhammad Tariq ◽  
Miao-Kun Wang
Keyword(s):  
Convex Function ◽  
Hypergeometric Function ◽  
Convex Functions ◽  
Special Functions ◽  
Integral Inequalities ◽  
Real Numbers ◽  
Algebraic Properties ◽  
Type Integral ◽  
Harmonically Convex Functions ◽  
Formula Type

In this work, we introduce the idea of n –polynomial harmonically s –type convex function. We elaborate the new introduced idea by examples and some interesting algebraic properties. As a result, new Hermite–Hadamard, some refinements of Hermite–Hadamard and Ostrowski type integral inequalities are established, which are the generalized variants of the previously known results for harmonically convex functions. Finally, we illustrate the applicability of this new investigation in special functions (hypergeometric function and special mean of real numbers).

scholarly journals Trapezoid and Midpoint Type Inequalities for Preinvex Functions via Quantum Calculus

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1666
Author(s):  
Surang Sitho ◽  
Muhammad Aamir Ali ◽  
Hüseyin Budak ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Type Inequality ◽  
Quantum Calculus ◽  
Proper Form ◽  
Quantum Integral ◽  
Preinvex Functions

In this article, we use quantum integrals to derive Hermite–Hadamard inequalities for preinvex functions and demonstrate their validity with mathematical examples. We use the qϰ2-quantum integral to show midpoint and trapezoidal inequalities for qϰ2-differentiable preinvex functions. Furthermore, we demonstrate with an example that the previously proved Hermite–Hadamard-type inequality for preinvex functions via qϰ1-quantum integral is not valid for preinvex functions, and we present its proper form. We use qϰ1-quantum integrals to show midpoint inequalities for qϰ1-differentiable preinvex functions. It is also demonstrated that by considering the limit q→1− and ηϰ2,ϰ1=−ηϰ1,ϰ2=ϰ2−ϰ1 in the newly derived results, the newly proved findings can be turned into certain known results.

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