scholarly journals Two-Variable Quantum Integral Inequalities of Simpson-Type Based on Higher-Order Generalized Strongly Preinvex and Quasi-Preinvex Functions

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 51 ◽  
Author(s):  
Humaira Kalsoom ◽  
Saima Rashid ◽  
Muhammad Idrees ◽  
Yu-Ming Chu ◽  
Dumitru Baleanu
Keyword(s):  
Integral Identity ◽  
Higher Order ◽  
Integral Inequalities ◽  
Numerical Approximations ◽  
New Class ◽  
Quantum Integral ◽  
Special Cases ◽  
Preinvex Functions ◽  
Definition Of

In this paper, we present a new definition of higher-order generalized strongly preinvex functions. Moreover, it is observed that the new class of higher-order generalized strongly preinvex functions characterize various new classes as special cases. We acquire a new q 1 q 2 -integral identity, then employing this identity, we establish several two-variable q 1 q 2 -integral inequalities of Simpson-type within a class of higher-order generalized strongly preinvex and quasi-preinvex functions. Finally, the utilities of our numerical approximations have concrete applications.

scholarly journals Quantum Integral Inequalities of Simpson-Type for Strongly Preinvex Functions

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 751 ◽  
Author(s):  
Yongping Deng ◽  
Muhammad Uzair Awan ◽  
Shanhe Wu
Keyword(s):  
Integral Identity ◽  
Integral Inequalities ◽  
Quantum Integral ◽  
Special Cases ◽  
Preinvex Functions

In this paper, we establish a new q-integral identity, the result is then used to derive two q-integral inequalities of Simpson-type involving strongly preinvex functions. Some special cases of the obtained results are also considered, it is shown that several new and previously known results can be derived via generalized strongly preinvex functions and quantum integrals.

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 Some New Postquantum Integral Inequalities

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Yu-Ming Chu ◽  
Muhammad Uzair Awan ◽  
Sadia Talib ◽  
Sabah Iftikhar ◽  
Latifa Riahi
Keyword(s):  
Integral Identity ◽  
Integral Inequalities ◽  
Auxiliary Result ◽  
Special Cases ◽  
Preinvex Functions

The goal of this paper is to derive a new generalized postquantum integral identity. Using this new identity as an auxiliary result, we derive some new variants of integral inequalities using p , q -differentiable preinvex functions. We also point out some special cases of the obtained results which show that our results are quite unifying ones.

scholarly journals Some Trapezium-Like Inequalities Involving Functions Having Strongly n-Polynomial Preinvexity Property of Higher Order

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Muhammad Uzair Awan ◽  
Sadia Talib ◽  
Muhammad Aslam Noor ◽  
Yu-Ming Chu ◽  
Khalida Inayat Noor
Keyword(s):  
Fractional Calculus ◽  
Higher Order ◽  
New Class ◽  
Special Cases ◽  
Preinvex Functions ◽  
Class Of Functions

The main objective of this paper is to introduce a new class of preinvex functions which is called as n-polynomial preinvex functions of a higher order. As applications of this class of functions, we discuss several new variants of trapezium-like inequalities. In order to obtain the main results of the paper, we use the concepts and techniques of k-fractional calculus. We also discuss some special cases of the obtained results which show that the main results of the paper are quite unifying one.

scholarly journals q -Hermite–Hadamard Inequalities for Generalized Exponentially s , m ; η -Preinvex Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Hua Wang ◽  
Humaira Kalsoom ◽  
Hüseyin Budak ◽  
Muhammad Idrees
Keyword(s):  
Differentiable Function ◽  
Integral Identity ◽  
Special Cases ◽  
Preinvex Functions ◽  
Definition Of ◽  
Classical Convexity

In this article, we introduce a new extension of classical convexity which is called generalized exponentially s , m ; η -preinvex functions. Also, it is seen that the new definition of generalized exponentially s , m ; η -preinvex functions describes different new classes as special cases. To prove our main results, we derive a new q m κ 2 -integral identity for the twice q m κ 2 -differentiable function. By using this identity, we show essential new results for Hermite–Hadamard-type inequalities for the q m κ 2 -integral by utilizing differentiable exponentially s , m ; η -preinvex functions. The results presented in this article are unification and generalization of the comparable results in the literature.

scholarly journals Some New Classes of Preinvex Functions and Inequalities

Mathematics ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. 29 ◽  
Author(s):  
Muhammad Noor ◽  
Khalida Noor ◽  
Saima Rashid
Keyword(s):  
Integral Inequalities ◽  
Auxiliary Functions ◽  
New Class ◽  
Special Cases ◽  
Preinvex Functions

In this article, we introduce some new class of preinvex functions involving two arbitrary auxiliary functions. We derive some new integral inequalities for these classes of preinvex functions. We also discuss some special cases which can be deduced from our main results.

scholarly journals On exponentially ϱ-preinvex functions and associated trapezium like inequalities

2021 ◽  
pp. 25-25
Author(s):  
Artion Kashuri ◽  
Muhammad Awan ◽  
Sadia Talib ◽  
Muhammad Noor ◽  
Khalida Noor
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
New Class ◽  
Special Cases ◽  
Preinvex Functions

In this paper, authors introduce a new extension of ?-convexity called ?- preinvexity and generalize the discussed results by Wu et al. in ?On a new class of convex functions and integral inequalities?. Some special cases are deduced from main results. At the end, a briefly conclusion is given.

scholarly journals A new q-integral identity and estimation of its bounds involving generalized exponentially μ-preinvex functions

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Muhammad Uzair Awan ◽  
Sadia Talib ◽  
Artion Kashuri ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor ◽  
...  
Keyword(s):  
Differentiable Function ◽  
Integral Identity ◽  
Second Order ◽  
Integral Inequalities ◽  
Absolute Value ◽  
Type Integral ◽  
Preinvex Functions

Abstract In the article, we introduce the generalized exponentially μ-preinvex function, derive a new q-integral identity for second order q-differentiable function, and establish several new q-trapezoidal type integral inequalities for the function whose absolute value of second q-derivative is exponentially μ-preinvex.

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 Fractional trapezium type inequalities for twice differentiable preinvex functions and their applications

2020 ◽  
Vol 10 (2) ◽  
pp. 226-236
Author(s):  
Artion Kashuri ◽  
Rozana Liko
Keyword(s):  
Integral Operator ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Recent Past ◽  
Trapezium Type ◽  
Special Means ◽  
Special Cases ◽  
Type Integral ◽  
Preinvex Functions ◽  
Almost All

Trapezoidal inequalities for functions of divers natures are useful in numerical computations. The authors have proved an identity for a generalized integral operator via twice differentiable preinvex function. By applying the established identity, the generalized trapezoidal type integral inequalities have been discovered. It is pointed out that the results of this research provide integral inequalities for almost all fractional integrals discovered in recent past decades. Various special cases have been identified. Some applications of presented results to special means have been analyzed. The ideas and techniques of this paper may stimulate further research.

Sign in / Sign up

Export Citation Format

Share Document