scholarly journals On Hermite-Hadamard Type Inequalities fors-Convex Functions on the Coordinates via Riemann-Liouville Fractional Integrals

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Feixiang Chen
Keyword(s):  
Convex Functions ◽  
Type Inequality ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Right Hand ◽  
The Right

We obtain some Hermite-Hadamard type inequalities fors-convex functions on the coordinates via Riemann-Liouville integrals. Some integral inequalities with the right-hand side of the fractional Hermite-Hadamard type inequality are also established.

scholarly journals On refinements of some integral inequalities for differentiable prequasiinvex functions

Filomat ◽  
2019 ◽  
Vol 33 (14) ◽  
pp. 4377-4385
Author(s):  
Serap Özcan
Keyword(s):  
Integral Inequality ◽  
Type Inequality ◽  
Integral Inequalities ◽  
Right Hand ◽  
The Right ◽  
New Inequalities ◽  
Better Than

In this paper, using the new and improved form of H?lder?s integral inequality called H?lder-??can integral inequality, some new inequalities of the right-hand side of Hermite-Hadamard type inequality for prequasiinvex functions are established. The results obtained are compared with the known results. It is shown that the results obtained in this paper are better than those known ones.

scholarly journals Fractional integral inequalities of Hermite-Hadamard type for convex functions with respect to a monotone function

Filomat ◽  
2020 ◽  
Vol 34 (7) ◽  
pp. 2401-2411
Author(s):  
Pshtiwan Mohammed
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Special Functions ◽  
Monotone Function ◽  
Type Inequality ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Increasing Functions

In the literature, the left-side of Hermite-Hadamard?s inequality is called a midpoint type inequality. In this article, we obtain new integral inequalities of midpoint type for Riemann-Liouville fractional integrals of convex functions with respect to increasing functions. The resulting inequalities generalize some recent integral inequalities and Riemann-Liouville fractional integral inequalities established in earlier works. Finally, applications of our work are demonstrated via the known special functions.

scholarly journals New Modifications of Integral Inequalities via ℘-Convexity Pertaining to Fractional Calculus and Their Applications

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1753
Author(s):  
Saima Rashid ◽  
Aasma Khalid ◽  
Omar Bazighifan ◽  
Georgia Irina Oros
Keyword(s):  
Integral Operator ◽  
Convex Functions ◽  
Hypergeometric Functions ◽  
Fractional Integral ◽  
Type Inequality ◽  
Fractional Integral Operator ◽  
Integral Inequalities ◽  
Convex Mappings ◽  
Special Cases ◽  
Harmonically Convex Functions

Integral inequalities for ℘-convex functions are established by using a generalised fractional integral operator based on Raina’s function. Hermite–Hadamard type inequality is presented for ℘-convex functions via generalised fractional integral operator. A novel parameterized auxiliary identity involving generalised fractional integral is proposed for differentiable mappings. By using auxiliary identity, we derive several Ostrowski type inequalities for functions whose absolute values are ℘-convex mappings. It is presented that the obtained outcomes exhibit classical convex and harmonically convex functions which have been verified using Riemann–Liouville fractional integral. Several generalisations and special cases are carried out to verify the robustness and efficiency of the suggested scheme in matrices and Fox–Wright generalised hypergeometric functions.

scholarly journals Some (p,q)-Estimates of Hermite-Hadamard-Type Inequalities for Coordinated Convex and Quasi- Convex Functions

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 683 ◽  
Author(s):  
Humaira Kalsoom ◽  
Muhammad Amer ◽  
Moin-ud-Din Junjua ◽  
Sabir Hussain ◽  
Gullnaz Shahzadi
Keyword(s):  
Convex Functions ◽  
Integral Type ◽  
Partial Derivatives ◽  
Functions Of Two Variables ◽  
Right Hand ◽  
The Absolute ◽  
The Right ◽  
Quasi Convexity

In this paper, we present the preliminaries of ( p , q ) -calculus for functions of two variables. Furthermore, we prove some new Hermite-Hadamard integral-type inequalities for convex functions on coordinates over [ a , b ] × [ c , d ] by using the ( p , q ) -calculus of the functions of two variables. Furthermore, we establish an identity for the right-hand side of the Hermite-Hadamard-type inequalities on coordinates that is proven by using the ( p , q ) -calculus of the functions of two variables. Finally, we use the new identity to prove some trapezoidal-type inequalities with the assumptions of convexity and quasi-convexity on coordinates of the absolute values of the partial derivatives defined in the ( p , q ) -calculus of the functions of two variables.

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 Generalized Hadamard Fractional Integral Inequalities for Strongly s , m -Convex Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Chao Miao ◽  
Ghulam Farid ◽  
Hafsa Yasmeen ◽  
Yanhua Bian
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Hadamard Inequality ◽  
Hadamard Fractional Integral

This article deals with Hadamard inequalities for strongly s , m -convex functions using generalized Riemann–Liouville fractional integrals. Several generalized fractional versions of the Hadamard inequality are presented; we also provide refinements of many known results which have been published in recent years.

scholarly journals Hadamard and Fejér–Hadamard Inequalities for Further Generalized Fractional Integrals Involving Mittag-Leffler Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
M. Yussouf ◽  
G. Farid ◽  
K. A. Khan ◽  
Chahn Yong Jung
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Harmonically Convex Functions

In this paper, generalized versions of Hadamard and Fejér–Hadamard type fractional integral inequalities are obtained. By using generalized fractional integrals containing Mittag-Leffler functions, some well-known results for convex and harmonically convex functions are generalized. The results of this paper are connected with various published fractional integral inequalities.

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