scholarly journals Generalizations of Wendroff Integral Inequalities and Their Discrete Analogues

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Maksat Ashyraliyev
Keyword(s):  
Goursat Problem ◽  
Integral Inequalities ◽  
Stability Estimates ◽  
Type Integral ◽  
Discrete Analogues ◽  
The Stability

Generalizations of Wendroff type integral inequalities with four dependent limits and their discrete analogues are obtained. In applications, these results are used to establish the stability estimates for the solution of the Goursat problem.

scholarly journals Explicit bounds on Gamidov type integral

2006 ◽  
Vol 37 (1) ◽  
pp. 1-9 ◽  
Author(s):  
B. G. Pachpatte
Keyword(s):  
Upper Bounds ◽  
Integral Inequalities ◽  
Type Integral ◽  
Explicit Bounds ◽  
Discrete Analogues

The aim of this paper is to establish explicit upper bounds on certain Gamidov type integral inequalities which can be used as convenient tools in some applications. The discrete analogues and applications are given to illustrate the usefulness of one of our results.

scholarly journals On Gronwall’s type integral inequalities with singular kernels

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 1041-1049 ◽  
Author(s):  
Maksat Ashyraliyev
Keyword(s):  
Differential Equation ◽  
Integral Equation ◽  
Fractional Differential Equations ◽  
Parabolic Type ◽  
Integral Inequalities ◽  
Stability Estimates ◽  
Type Integral ◽  
Singular Kernels ◽  
Fractional Differential ◽  
Integral Differential Equation

In this paper, the generalizations of Gronwall?s type integral inequalities with singular kernels are established. In applications, theorems on stability estimates for the solutions of the nonliner integral equation and the integral-differential equation of the parabolic type are presented. Moreover, these inequalities can be used in the theory of fractional differential equations.

scholarly journals Fractional Integral Inequalities for Exponentially Nonconvex Functions and Their Applications

2021 ◽  
Vol 5 (3) ◽  
pp. 80
Author(s):  
Hari Mohan Srivastava ◽  
Artion Kashuri ◽  
Pshtiwan Othman Mohammed ◽  
Dumitru Baleanu ◽  
Y. S. Hamed
Keyword(s):  
Integral Inequalities ◽  
Fractional Integrals ◽  
Auxiliary Result ◽  
Wright Function ◽  
Nonconvex Functions ◽  
Special Cases ◽  
Type Integral ◽  
Generic Class ◽  
Two Parameters ◽  
Class Of Functions

In this paper, the authors define a new generic class of functions involving a certain modified Fox–Wright function. A useful identity using fractional integrals and this modified Fox–Wright function with two parameters is also found. Applying this as an auxiliary result, we establish some Hermite–Hadamard-type integral inequalities by using the above-mentioned class of functions. Some special cases are derived with relevant details. Moreover, in order to show the efficiency of our main results, an application for error estimation is obtained as well.

scholarly journals Some Hermite–Hadamard type integral inequalities for convex functions defined on convex bodies in ℝn\mathbb{R}^{n}

2020 ◽  
Vol 26 (1) ◽  
pp. 67-77 ◽  
Author(s):  
Silvestru Sever Dragomir
Keyword(s):  
Euclidean Space ◽  
Convex Functions ◽  
Convex Bodies ◽  
Integral Inequalities ◽  
Divergence Theorem ◽  
Several Variables ◽  
Type Integral ◽  
Bounded Convex

AbstractIn this paper, by the use of the divergence theorem, we establish some integral inequalities of Hermite–Hadamard type for convex functions of several variables defined on closed and bounded convex bodies in the Euclidean space {\mathbb{R}^{n}} for any {n\geq 2}.

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 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.

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