scholarly journals Inequalities for Estimations of Integrals Related to Higher-Order Strongly n -Polynomial Preinvex Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Yongping Deng ◽  
Muhammad Uzair Awan ◽  
Sadia Talib ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor ◽  
...  
Keyword(s):  
Integral Identity ◽  
Higher Order ◽  
Differentiable Functions ◽  
Special Means ◽  
Preinvex Functions ◽  
New Inequalities

In this paper, we establish an integral identity associated with m -times differentiable functions. The result is then used to derive some integral estimations for higher-order strongly n -polynomial preinvex functions. Finally, we apply the obtained inequalities to construct new inequalities involving special means.

scholarly journals Some New Post-Quantum Integral Inequalities Involving Twice (p,q)-Differentiable ψ-Preinvex Functions and Applications

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 283
Author(s):  
Miguel Vivas-Cortez ◽  
Muhammad Uzair Awan ◽  
Sadia Talib ◽  
Artion Kashuri ◽  
Muhammad Aslam Noor
Keyword(s):  
Integral Identity ◽  
Auxiliary Result ◽  
Real Numbers ◽  
Positive Real ◽  
Main Motivation ◽  
Absolute Value ◽  
Differentiable Functions ◽  
Quantum Integral ◽  
Special Means ◽  
Preinvex Functions

The main motivation of this article is derive a new post-quantum integral identity using twice (p,q)-differentiable functions. Using the identity as an auxiliary result, we will obtain some new variants of Hermite–Hadamard’s inequality essentially via the class of ψ-preinvex functions. To support our results, we offer some applications to a special means of positive real numbers and twice (p,q)-differentiable functions that are in absolute value bounded as well.

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 Estimations of Upper Bounds for n -th Order Differentiable Functions Involving χ -Riemann–Liouville Integrals via γ -Preinvex Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Sadia Talib ◽  
Muhammad Uzair Awan
Keyword(s):  
Integral Identity ◽  
Fractional Integral ◽  
Upper Bounds ◽  
Fractional Integrals ◽  
Differentiable Functions ◽  
Special Cases ◽  
Preinvex Functions

A new fractional integral identity is obtained involving n -th order differentiable functions and χ -Riemann–Liouville fractional integrals. Then, some associated estimates of upper bounds involving γ -preinvex functions are obtained. In order to relate some unrelated results, several special cases are discussed.

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 Fractional Integral Inequalities for Strongly h -Preinvex Functions for a kth Order Differentiable Functions

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1448 ◽  
Author(s):  
Saima Rashid ◽  
Muhammad Amer Latif ◽  
Zakia Hammouch ◽  
Yu-Ming Chu
Keyword(s):  
Integral Operator ◽  
Differentiable Function ◽  
Real World ◽  
Fractional Integral ◽  
Higher Order ◽  
Fractional Integrals ◽  
Differentiable Functions ◽  
Real World Applications ◽  
Mathematical Problems ◽  
Preinvex Functions

The objective of this paper is to derive Hermite-Hadamard type inequalities for several higher order strongly h -preinvex functions via Riemann-Liouville fractional integrals. These results are the generalizations of the several known classes of preinvex functions. An identity associated with k-times differentiable function has been established involving Riemann-Liouville fractional integral operator. A number of new results can be deduced as consequences for the suitable choices of the parameters h and σ . Our outcomes with these new generalizations have the abilities to be implemented for the evaluation of many mathematical problems related to real world applications.

scholarly journals Some New Inequalities on Generalization of Hermite-Hadamard and Bullen Type Inequalities, Applications to Trapezoidal and Midpoint Formula

2021 ◽  
Vol 45 (4) ◽  
pp. 647-657
Author(s):  
İMDAT İŞCAN ◽  
◽  
TEKİN TOPLU ◽  
FATİH YETGİN ◽  
◽  
...  
Keyword(s):  
Error Estimates ◽  
Real Numbers ◽  
Absolute Value ◽  
General Identity ◽  
Differentiable Functions ◽  
Special Means ◽  
New Inequalities

In this paper, we give a new general identity for differentiable functions. A consequence of the identity is that we obtain some new general inequalities containing all of the Hermite-Hadamard and Bullen type for functions whose derivatives in absolute value at certain power are convex. Some applications to special means of real numbers are also given. Finally, some error estimates for the trapezoidal and midpoint formula are addressed.

scholarly journals On post quantum estimates of upper bounds involving twice $(p,q)$-differentiable preinvex function

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Muhammad Uzair Awan ◽  
Sadia Talib ◽  
Muhammad Aslam Noor ◽  
Yu-Ming Chu ◽  
Khalida Inayat Noor
Keyword(s):  
Integral Identity ◽  
Upper Bounds ◽  
Auxiliary Result ◽  
Differentiable Functions ◽  
Quantum Integral ◽  
Preinvex Functions

Abstract The main objective of this paper is to derive a new post quantum integral identity using twice $(p,q)$ ( p , q ) -differentiable functions. Using this identity as an auxiliary result, we obtain some new post quantum estimates of upper bounds involving twice $(p,q)$ ( p , q ) -differentiable preinvex functions.

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.

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