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 New Estimates of q1q2-Ostrowski-Type Inequalities within a Class of n-Polynomial Prevexity of Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-13 ◽  
Author(s):  
Humaira Kalsoom ◽  
Muhammad Idrees ◽  
Dumitru Baleanu ◽  
Yu-Ming Chu
Keyword(s):  
Differentiable Function ◽  
Nonnegative Function ◽  
Integral Inequalities ◽  
Quantum Calculus ◽  
New Class ◽  
Type Integral ◽  
Preinvex Functions

In this article, we develop a novel framework to study for a new class of preinvex functions depending on arbitrary nonnegative function, which is called n-polynomial preinvex functions. We use the n-polynomial preinvex functions to develop q1q2-analogues of the Ostrowski-type integral inequalities on coordinates. Different features and properties of excitement for quantum calculus have been examined through a systematic way. We are discussing about the suggestions and different results of the quantum inequalities of the Ostrowski-type by inferring a new identity for q1q2-differentiable function. However, the problem has been proven to utilize the obtained identity, we give q1q2-analogues of the Ostrowski-type integrals inequalities which are connected with the n-polynomial preinvex functions on coordinates. Our results are the generalizations of the results in earlier papers.

scholarly journals Fractional integral identity, estimation of its bounds and some applications to trapezoidal quadrature rule

Filomat ◽  
2020 ◽  
Vol 34 (8) ◽  
pp. 2629-2641
Author(s):  
Artion Kashuri ◽  
Muhammad Awan ◽  
Muhammad Noor
Keyword(s):  
Applied Sciences ◽  
Integral Identity ◽  
Fractional Integral ◽  
Quadrature Rule ◽  
The Other ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Trapezium Type ◽  
Type Integral ◽  
Preinvex Functions

The aim of this paper is to introduce a new extension of preinvexity called exponentially (m,?1,?2, h1,h2)-preinvexity. Some new integral inequalities of Hermite-Hadamard type for exponentially (m,?1,?2,h1,h2)-preinvex functions via Riemann-Liouville fractional integral are established. Also, some new estimates with respect to trapezium-type integral inequalities for exponentially (m,?1,?2,h1,h2)-preinvex functions via general fractional integrals are obtained. We show that the class of exponentially (m,?1,?2, h1,h2)-preinvex functions includes several other classes of preinvex functions. We shown by two basic examples the efficiency of the obtained inequalities on the base of comparing those with the other corresponding existing ones. At the end, some new error estimates for trapezoidal quadrature formula are provided as well. This results may stimulate further research in different areas of pure and applied sciences.

Some weighted integral inequalities for differentiable h-preinvex functions

2018 ◽  
Vol 25 (3) ◽  
pp. 441-450 ◽  
Author(s):  
Muhammad Amer Latif ◽  
Sever Silvestru Dragomir ◽  
Ebrahim Momoniat
Keyword(s):  
Integral Inequality ◽  
Integral Inequalities ◽  
Real Numbers ◽  
Absolute Value ◽  
Type Integral ◽  
Weighted Integral ◽  
Preinvex Functions ◽  
Special Case

AbstractIn this paper, by using a weighted identity for functions defined on an open invex subset of the set of real numbers, by using the Hölder integral inequality and by using the notion of h-preinvexity, we present weighted integral inequalities of Hermite–Hadamard-type for functions whose derivatives in absolute value raised to certain powers are h-preinvex functions. Some new Hermite–Hadamard-type integral inequalities are obtained when h is super-additive. Inequalities of Hermite–Hadamard-type for s-preinvex functions are given as well as a special case of our results.

scholarly journals Some Hermite-Hadamard type integral inequalities for operator AG-preinvex functions

2016 ◽  
Vol 8 (2) ◽  
pp. 312-323
Author(s):  
Ali Taghavi ◽  
Haji Mohammad Nazari ◽  
Vahid Darvish
Keyword(s):  
Integral Inequalities ◽  
Unitarily Invariant Norm ◽  
Norm Inequalities ◽  
Invariant Norm ◽  
Type Integral ◽  
Preinvex Functions ◽  
Inequalities For Operators

Abstract In this paper, we introduce the concept of operator AG-preinvex functions and prove some Hermite-Hadamard type inequalities for these functions. As application, we obtain some unitarily invariant norm inequalities for operators.

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.

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 Fejér type integral inequalities related with geometrically-arithmetically convex functions with applications

2019 ◽  
Vol 23 (1) ◽  
pp. 51-64
Author(s):  
S. S. Dragomir ◽  
M. A. Latif ◽  
E. Momoniat
Keyword(s):  
Differentiable Function ◽  
Integral Inequality ◽  
Convex Functions ◽  
Symmetric Function ◽  
Integral Inequalities ◽  
Real Numbers ◽  
Positive Real ◽  
Left Part ◽  
Special Means ◽  
Type Integral

A new identity involving a geometrically symmetric function and a differentiable function is established. Some new Fejér type integral inequalities, connected with the left part of Hermite–Hadamard type inequalities for geometrically-arithmetically convex functions, are presented by using the Hölder integral inequality and the notion of geometrically-arithmetically convexity. Applications of our results to special means of positive real numbers are given.

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