scholarly journals Generalized Integral Inequalities for Hermite-Hadamard Type via s-Convexity on Fractal Sets

2019 ◽  
Author(s):  
Ohud Almutairi ◽  
Adem Kilicman
Keyword(s):  
Integral Inequalities ◽  
Fractal Sets ◽  
Second Derivatives ◽  
The Absolute ◽  
New Inequalities ◽  
Generalized Integral Inequalities

In this article, the new Hermite–Hadamard type inequalities are studied via generalized s-convexity on fractal sets. These inequalities derived on fractal sets are shown to be the generalized s-convexity on fractal sets. We proved that the absolute values of the first and second derivatives for the new inequalities are the generalization of s-convexity on fractal sets.

scholarly journals Generalized Integral Inequalities for Hermite-Hadamard Type via s-Convexity on Fractal Sets

2019 ◽  
Author(s):  
Ohud Almutairi ◽  
Adem Kilicman
Keyword(s):  
Integral Inequalities ◽  
Fractal Sets ◽  
Second Derivatives ◽  
The Absolute ◽  
New Inequalities ◽  
Generalized Integral Inequalities

In this article, the new Hermite–Hadamard type inequalities are studied via generalized s-convexity on fractal sets. These inequalities derived on fractal sets are shown to be the generalized s-convexity on fractal sets. We proved that the absolute values of the first and second derivatives for the new inequalities are the generalization of s-convexity on fractal sets.

scholarly journals New fractional inequalities of midpoint type via s-convexity and their application

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Ohud Almutairi ◽  
Adem Kılıçman
Keyword(s):  
Error Estimates ◽  
Integral Inequalities ◽  
Real Numbers ◽  
Special Means ◽  
Second Derivatives ◽  
The Absolute ◽  
New Inequalities

Abstract In this study, we introduced new integral inequalities of Hermite–Hadamard type via s-convexity and studied their properties. The absolute form of the first and second derivatives for the new inequalities is considered to be s-convex. As an application, the inequalities were applied to the special means of real numbers. We give the error estimates for the midpoint formula.

scholarly journals Generalized Integral Inequalities for Hermite–Hadamard-Type Inequalities via s-Convexity on Fractal Sets

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1065 ◽  
Author(s):  
Ohud Almutairi ◽  
Adem Kılıçman
Keyword(s):  
Second Order ◽  
Integral Inequalities ◽  
Order Derivative ◽  
Convexity Property ◽  
Absolute Value ◽  
Fractal Sets ◽  
The Absolute ◽  
Generalized Integral Inequalities

In this article, we establish new Hermite–Hadamard-type inequalities via Riemann–Liouville integrals of a function ψ taking its value in a fractal subset of R and possessing an appropriate generalized s-convexity property. It is shown that these fractal inequalities give rise to a generalized s-convexity property of ψ . We also prove certain inequalities involving Riemann–Liouville integrals of a function ψ provided that the absolute value of the first or second order derivative of ψ possesses an appropriate fractal s-convexity property.

Some new generalizations for GA-convex functions

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 1009-1016 ◽  
Author(s):  
Ahmet Akdemir ◽  
Özdemir Emin ◽  
Ardıç Avcı ◽  
Abdullatif Yalçın
Keyword(s):  
Convex Functions ◽  
Integral Identity ◽  
Integral Inequalities ◽  
General Integral ◽  
Second Derivatives ◽  
Derivatives Of

In this paper, firstly we prove an integral identity that one can derive several new equalities for special selections of n from this identity: Secondly, we established more general integral inequalities for functions whose second derivatives of absolute values are GA-convex functions based on this equality.

scholarly journals On New Inequalities of Simpson’s Type for Functions Whose Second Derivatives Absolute Values are Convex

2013 ◽  
Vol 9 (1) ◽  
pp. 37-45 ◽  
Author(s):  
Mehmet Zeki Sarikaya ◽  
Erhan. Set ◽  
M. Emin Ozdemir
Keyword(s):  
Real Numbers ◽  
Special Means ◽  
Second Derivatives ◽  
New Inequalities

Abstract In this note, we obtain new some inequalities of Simpson’s type based on convexity. Some applications for special means of real numbers are also given.

scholarly journals New inequalities of Hermite-Hadamard type for n-times differentiable convex and concave functions with applications

Filomat ◽  
2016 ◽  
Vol 30 (10) ◽  
pp. 2609-2621
Author(s):  
M.A. Latif ◽  
S.S. Dragomir
Keyword(s):  
Concave Functions ◽  
Absolute Value ◽  
Trapezoidal Formula ◽  
Special Means ◽  
Second Derivatives ◽  
Special Cases ◽  
New Inequalities

In this paper, a new identity for n-times differntiable functions is established and by using the obtained identity, some new inequalities Hermite-Hadamard type are obtained for functions whose nth derivatives in absolute value are convex and concave functions. From our results, several inequalities of Hermite-Hadamard type can be derived in terms of functions whose first and second derivatives in absolute value are convex and concave functions as special cases. Our results may provide refinements of some results already exist in literature. Applications to trapezoidal formula and special means of established results are given.

scholarly journals On certain new CAUCHY–TYPE fracitioanl integral inequalities and OPIAL–TYPE fractional derivative inequalities

2015 ◽  
Vol 46 (1) ◽  
pp. 67-73 ◽  
Author(s):  
Amit Chouhan
Keyword(s):  
Fractional Derivative ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Future Research ◽  
Cauchy Type ◽  
Fractional Integral Operators ◽  
Integrable Functions ◽  
New Inequalities

The aim of this paper is to establish several new fractional integral and derivative inequalities for non-negative and integrable functions. These inequalities related to the extension of general Cauchy type inequalities and involving Saigo, Riemann-Louville type fractional integral operators together with multiple Erdelyi-Kober operator. Furthermore the Opial-type fractional derivative inequality involving H-function is also established. The generosity of H-function could leads to several new inequalities that are of great interest of future research.

scholarly journals Some New Tempered Fractional Pólya-Szegö and Chebyshev-Type Inequalities with Respect to Another Function

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Gauhar Rahman ◽  
Kottakkaran Sooppy Nisar ◽  
Thabet Abdeljawad ◽  
Muhammad Samraiz
Keyword(s):  
Present Article ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Bounded Functions ◽  
New Inequalities

In this present article, we establish certain new Pólya–Szegö-type tempered fractional integral inequalities by considering the generalized tempered fractional integral concerning another function Ψ in the kernel. We then prove certain new Chebyshev-type tempered fractional integral inequalities for the said operator with the help of newly established Pólya–Szegö-type tempered fractional integral inequalities. Also, some new particular cases in the sense of classical tempered fractional integrals are discussed. Additionally, examples of constructing bounded functions are considered. Furthermore, one can easily form new inequalities for Katugampola fractional integrals, generalized Riemann–Liouville fractional integral concerning another function Ψ in the kernel, and generalized fractional conformable integral by applying different conditions.

scholarly journals New Inequalities for Strongly r-Convex Functions

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Huriye Kadakal
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Integral Identity ◽  
Integral Inequalities ◽  
Special Cases ◽  
Class Of Functions ◽  
New Inequalities

In this study, firstly we introduce a new concept called “strongly r-convex function.” After that we establish Hermite-Hadamard-like inequalities for this class of functions. Moreover, by using an integral identity together with some well known integral inequalities, we establish several new inequalities for n-times differentiable strongly r-convex functions. In special cases, the results obtained coincide with the well-known results in the literature.

Sign in / Sign up

Export Citation Format

Share Document