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 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 Ostrowski-type inequalities for n-polynomial $\mathscr{P}$-convex function for k-fractional Hilfer–Katugampola derivative

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Samaira Naz ◽  
Muhammad Nawaz Naeem ◽  
Yu-Ming Chu
Keyword(s):  
Fractional Calculus ◽  
Convex Function ◽  
Convex Functions ◽  
Special Functions ◽  
Integral Inequalities ◽  
Power Mean ◽  
New Class ◽  
Special Means ◽  
New Directions ◽  
Type Integral

AbstractIn this article, we develop a novel framework to study a new class of convex functions known as n-polynomial $\mathscr{P} $ P -convex functions. The purpose of this article is to establish a new generalization of Ostrowski-type integral inequalities by using a generalized k-fractional Hilfer–Katugampola derivative. We employ this technique by using the Hölder and power-mean integral inequalities. We present analogs of the Ostrowski-type integrals inequalities connected with the n-polynomial $\mathscr{P}$ P -convex function. Some new exceptional cases from the main results are obtained, and some known results are recaptured. In the end, an application to special means is given as well. The article seeks to create an exciting combination of a convex function and special functions in fractional calculus. It is supposed that this investigation will provide new directions in fractional calculus.

scholarly journals Two point trapezoidal like inequalities involving hypergeometric functions

Filomat ◽  
2017 ◽  
Vol 31 (8) ◽  
pp. 2281-2292 ◽  
Author(s):  
Muhammad Awan ◽  
Muhammad Noor ◽  
Marcela Mihai ◽  
Khalida Noor
Keyword(s):  
Differentiable Function ◽  
Convex Functions ◽  
Integral Identity ◽  
Hypergeometric Functions ◽  
Auxiliary Result ◽  
Special Cases

In this paper, we derive a new integral identity for differentiable function. Using this new integral identity as an auxiliary result, we derive some new two point trapezoidal like inequalities for differentiable harmonic h-convex functions. These inequalities can also be viewed as Hermite-Hadamard type inequalities. We also discuss some new special cases which can be deduced from our main results.

scholarly journals Quantum Estimates of Ostrowski Inequalities for Generalized ϕ-Convex Functions

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1513 ◽  
Author(s):  
Miguel J. Vivas-Cortez ◽  
Artion Kashuri ◽  
Rozana Liko ◽  
Jorge E. Hernández Hernández
Keyword(s):  
Convex Functions ◽  
Convex Sets ◽  
Special Function ◽  
Special Functions ◽  
Quantum Calculus ◽  
Differentiable Functions ◽  
Basic Concepts

In this paper, the study is focused on the quantum estimates of Ostrowski type inequalities for q-differentiable functions involving the special function introduced by R.K. Raina which depends on certain parameters. Our methodology involves Jackson’s q-integral, the basic concepts of quantum calculus, and a generalization of a class of special functions used in the frame of convex sets and convex functions. As a main result, some quantum estimates for the aforementioned inequality are established and some cases involving the special hypergeometric and Mittag–Leffler functions have been studied and some known results are deduced.

scholarly journals New fractional approaches for n-polynomial P-convexity with applications in special function theory

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shu-Bo Chen ◽  
Saima Rashid ◽  
Muhammad Aslam Noor ◽  
Zakia Hammouch ◽  
Yu-Ming Chu
Keyword(s):  
Fractional Calculus ◽  
Convex Functions ◽  
Special Functions ◽  
Real Life ◽  
Fractional Integrals ◽  
Digamma Function ◽  
Novel Approach ◽  
Inequality Theory ◽  
New Strategy ◽  
Significant Mechanism

Abstract Inequality theory provides a significant mechanism for managing symmetrical aspects in real-life circumstances. The renowned distinguishing feature of integral inequalities and fractional calculus has a solid possibility to regulate continuous issues with high proficiency. This manuscript contributes to a captivating association of fractional calculus, special functions and convex functions. The authors develop a novel approach for investigating a new class of convex functions which is known as an n-polynomial $\mathcal{P}$ P -convex function. Meanwhile, considering two identities via generalized fractional integrals, provide several generalizations of the Hermite–Hadamard and Ostrowski type inequalities by employing the better approaches of Hölder and power-mean inequalities. By this new strategy, using the concept of n-polynomial $\mathcal{P}$ P -convexity we can evaluate several other classes of n-polynomial harmonically convex, n-polynomial convex, classical harmonically convex and classical convex functions as particular cases. In order to investigate the efficiency and supremacy of the suggested scheme regarding the fractional calculus, special functions and n-polynomial $\mathcal{P}$ P -convexity, we present two applications for the modified Bessel function and $\mathfrak{q}$ q -digamma function. Finally, these outcomes can evaluate the possible symmetric roles of the criterion that express the real phenomena of the problem.

scholarly journals New fractional inequalities of Hermite–Hadamard type involving the incomplete gamma functions

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Pshtiwan Othman Mohammed ◽  
Thabet Abdeljawad ◽  
Dumitru Baleanu ◽  
Artion Kashuri ◽  
Faraidun Hamasalh ◽  
...  
Keyword(s):  
Convex Functions ◽  
Special Functions ◽  
Integral Inequalities ◽  
Fractional Operators ◽  
Gamma Functions ◽  
Incomplete Gamma Functions ◽  
Type Integral

AbstractA specific type of convex functions is discussed. By examining this, we investigate new Hermite–Hadamard type integral inequalities for the Riemann–Liouville fractional operators involving the generalized incomplete gamma functions. Finally, we expose some examples of special functions to support the usefulness and effectiveness of our results.

scholarly journals Some new Simpson-type inequalities for generalized p-convex function on fractal sets with applications

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Thabet Abdeljawad ◽  
Saima Rashid ◽  
Zakia Hammouch ◽  
İmdat İşcan ◽  
Yu-Ming Chu
Keyword(s):  
Convex Functions ◽  
Fractional Derivatives ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Auxiliary Result ◽  
Fractal Sets ◽  
Different Types ◽  
Novel Applications ◽  
Class Of Functions ◽  
Harmonically Convex Functions

Abstract The present article addresses the concept of p-convex functions on fractal sets. We are able to prove a novel auxiliary result. In the application aspect, the fidelity of the local fractional is used to establish the generalization of Simpson-type inequalities for the class of functions whose local fractional derivatives in absolute values at certain powers are p-convex. The method we present is an alternative in showing the classical variants associated with generalized p-convex functions. Some parts of our results cover the classical convex functions and classical harmonically convex functions. Some novel applications in random variables, cumulative distribution functions and generalized bivariate means are obtained to ensure the correctness of the present results. The present approach is efficient, reliable, and it can be used as an alternative to establishing new solutions for different types of fractals in computer graphics.

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 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 A Quantum Approach to the Psychosomatic Phenomenon: Co-Emergence and Time Entanglement of Mind and Matter

KronoScope ◽  
2012 ◽  
Vol 12 (2) ◽  
pp. 219-244 ◽  
Author(s):  
Pierre Uzan
Keyword(s):  
Quantum Theory ◽  
Physical World ◽  
Neutral Monism ◽  
Quantum Approach ◽  
The Individual

AbstractThis paper explores the philosophy of neutral monism within the framework of a generalized version of quantum theory where all references to the physical world have been relaxed. Psychic and somatic features of the individual are conceived of as co-emergent, complementary properties of an underlying, psychophysical level of reality. It is shown that their entanglement can be interpreted in terms of non-causal correlations and parameterized by time, which thus plays the role of psychophysical interface.

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