scholarly journals Q-Analogue of Holder’s and Minkowski’s Integral Inequalities on Finite Intervals and Generalization

2021 ◽  
Vol 6 ◽  
pp. 235-243
Author(s):  
Suresh Bhatta ◽  
Chet Raj Bhatta
Keyword(s):  
Integral Inequality ◽  
Finite Interval ◽  
Integral Inequalities ◽  
Hölder’S Integral Inequality

In recent years, the topic on Holder’s and Minkowski’s inequalities has been studied by several researchers and variety of new results has been developed on their variants, extensions and generalizations. In this paper we give the extension to the generalized q- Holder’s integral inequality and by using it we also establish the generalization on q- Minkowski’s integral inequality on the finite interval [a, b]

scholarly journals New Integral Inequalities via Generalized Preinvex Functions

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 296
Author(s):  
Muhammad Tariq ◽  
Asif Ali Shaikh ◽  
Soubhagya Kumar Sahoo ◽  
Hijaz Ahmad ◽  
Thanin Sitthiwirattham ◽  
...  
Keyword(s):  
Integral Inequality ◽  
Type Inequality ◽  
Integral Inequalities ◽  
Power Mean ◽  
Science And Engineering ◽  
Special Means ◽  
Algebraic Properties ◽  
Convexity Theory ◽  
Hölder’S Integral Inequality ◽  
Preinvex Functions

The theory of convexity plays an important role in various branches of science and engineering. The objective of this paper is to introduce a new notion of preinvex functions by unifying the n-polynomial preinvex function with the s-type m–preinvex function and to present inequalities of the Hermite–Hadamard type in the setting of the generalized s-type m–preinvex function. First, we give the definition and then investigate some of its algebraic properties and examples. We also present some refinements of the Hermite–Hadamard-type inequality using Hölder’s integral inequality, the improved power-mean integral inequality, and the Hölder-İşcan integral inequality. Finally, some results for special means are deduced. The results established in this paper can be considered as the generalization of many published results of inequalities and convexity theory.

scholarly journals Some integral inequalities for approximately h—convex functions and their applications

2021 ◽  
Vol 40 (2) ◽  
pp. 481-504
Author(s):  
Artion Kashuri ◽  
Muhammad Raees ◽  
Matloob Anwar
Keyword(s):  
Convex Function ◽  
Integral Inequality ◽  
Convex Functions ◽  
Integral Inequalities ◽  
Integral Type ◽  
Special Cases ◽  
Hölder’S Integral Inequality ◽  
Error Estimations

In this paper, by applying the new and improved form of Hölder’s integral inequality called Hölder—Íşcan integral inequality three inequalities of Hermite—Hadamard and Hadamard integral type for (h, d)—convex functions have been established. Various special cases including classes for instance, h—convex, s—convex function of Breckner and Godunova—Levin—Dragomir and strong versions of the aforementioned types of convex functions have been identified. Some applications to error estimations of presented results have been analyzed. At the end, a briefly conclusion is given.

scholarly journals On Generalized Opial's Integral Inequalities in q-Calculus

2020 ◽  
pp. 106-114
Author(s):  
B. Abubakari ◽  
M. M. Iddrisu ◽  
K. Nantomah
Keyword(s):  
Integral Inequality ◽  
Integral Inequalities ◽  
Hölder’S Integral Inequality

In this paper, we establish results for q-analogues of generalized Opial integral inequalities and also present some extensions of the analogues. Using the concepts of q-differentiability and continuity of functions and the application of the Holder's integral inequality we establish the results.

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 k-fractional extension of Grüss-type inequalities via generalized Hilfer–Katugampola derivative

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Samaira Naz ◽  
Muhammad Nawaz Naeem ◽  
Yu-Ming Chu
Keyword(s):  
Integral Inequality ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Derivative Operator ◽  
Practical Applications ◽  
Mathematical Problems ◽  
Grüss Type Inequalities

AbstractIn this paper, we prove several inequalities of the Grüss type involving generalized k-fractional Hilfer–Katugampola derivative. In 1935, Grüss demonstrated a fascinating integral inequality, which gives approximation for the product of two functions. For these functions, we develop some new fractional integral inequalities. Our results with this new derivative operator are capable of evaluating several mathematical problems relevant to practical applications.

scholarly journals Generalizations and applications of Young’s integral inequality by higher order derivatives

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Jun-Qing Wang ◽  
Bai-Ni Guo ◽  
Feng Qi
Keyword(s):  
Differential Geometry ◽  
Integral Inequality ◽  
Higher Order ◽  
Integral Inequalities ◽  
List Type ◽  
Definite Integral ◽  
Exponential Integral ◽  
Definite Integrals ◽  
Logarithmic Integral

Abstract In the paper, the authors generalize Young’s integral inequality via Taylor’s theorems in terms of higher order derivatives and their norms, and apply newly-established integral inequalities to estimate several concrete definite integrals, including a definite integral of a function which plays an indispensable role in differential geometry and has a connection with the Lah numbers in combinatorics, the exponential integral, and the logarithmic integral.

scholarly journals A Generalization on Some New Types of Hardy-Hilbert’s Integral Inequalities

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Banyat Sroysang
Keyword(s):  
Weight Function ◽  
Integral Inequality ◽  
Integral Inequalities

Sulaiman presented, in 2008, new kinds of Hardy-Hilbert’s integral inequality in which the weight function is homogeneous. In this paper, we present a generalization on the kinds of Hardy-Hilbert’s integral inequality.

On Some Integral Inequalities Related to Hardy's

1977 ◽  
Vol 20 (3) ◽  
pp. 307-312 ◽  
Author(s):  
Christopher Olutunde Imoru
Keyword(s):  
Integral Inequality ◽  
Convex Functions ◽  
Jensen’S Inequality ◽  
Integral Inequalities ◽  
Hardy’S Inequality ◽  
Jensen's Inequality ◽  
Hardy's Inequality ◽  
Special Case

AbstractWe obtain mainly by using Jensen's inequality for convex functions an integral inequality, which contains as a special case Shun's generalization of Hardy's inequality.

Nonlinear integral inequalities of the Volterra type

1992 ◽  
Vol 111 (3) ◽  
pp. 599-608 ◽  
Author(s):  
Ryszard Szwarc
Keyword(s):  
Power Function ◽  
Integral Inequality ◽  
Integral Inequalities ◽  
Volterra Type ◽  
Identity Function ◽  
Right Hand ◽  
Half Axis ◽  
Image Position ◽  
The Right ◽  
Zero Points

We are studying the integral inequalitywhere all functions appearing are defined and increasing on the right half-axis and take the value zero at zero. We are interested in determining when the inequality admits solutions u(x) which are non-vanishing in a neighbourhood of zero. It is well-known that if ψ(x) is the identity function then no such solution exists. This due to the fact that the operator defined by the integral on the right-hand side of the equation is linear and compact. So if we are interested in non-trivial solutions it is natural to require that ψ(x) > 0 at least for all non-zero points in some neighbourhood of zero. One of the typical examples is the power function ψ(x) = xα, where α < 1. This situation was explored in [2]. The functions a(x) that admit non-zero solutions were characterized by Bushell in [1]. For a general approach to the problem we refer to [2], [3] and [4].

scholarly journals GENERALISATIONS OF INTEGRAL INEQUALITIES OF HERMITE–HADAMARD TYPE THROUGH CONVEXITY

2012 ◽  
Vol 88 (2) ◽  
pp. 320-330 ◽  
Author(s):  
MUHAMMAD MUDDASSAR ◽  
MUHAMMAD IQBAL BHATTI ◽  
WAJEEHA IRSHAD
Keyword(s):  
Numerical Integration ◽  
Integral Inequality ◽  
Integral Inequalities ◽  
Special Means ◽  
Differentiable Mappings

AbstractIn this paper, we establish various inequalities for some differentiable mappings that are linked with the illustrious Hermite–Hadamard integral inequality for mappings whose derivatives are $s$-$(\alpha , m)$-convex. The generalised integral inequalities contribute better estimates than some already presented. The inequalities are then applied to numerical integration and some special means.

Sign in / Sign up

Export Citation Format

Share Document