On some generalized integral inequalities for functions whose second derivatives in absolute values are convex

2021 ◽  
Author(s):  
Erhan Set ◽  
Alper Ekinci
Keyword(s):  
Integral Inequalities ◽  
Second Derivatives ◽  
Generalized Integral Inequalities

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.

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 general versions of Hermite–Hadamard type integral inequalities via fractional integral operators with Mittag-Leffler kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Havva Kavurmacı Önalan ◽  
Ahmet Ocak Akdemir ◽  
Merve Avcı Ardıç ◽  
Dumitru Baleanu
Keyword(s):  
Integral Equation ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Fractional Integral Operators ◽  
Frequency Of Use ◽  
Second Derivatives ◽  
New Variant ◽  
Type Integral ◽  
Basic Concepts

AbstractThe main motivation of this study is to bring together the field of inequalities with fractional integral operators, which are the focus of attention among fractional integral operators with their features and frequency of use. For this purpose, after introducing some basic concepts, a new variant of Hermite–Hadamard (HH-) inequality is obtained for s-convex functions in the second sense. Then, an integral equation, which is important for the main findings, is proved. With the help of this integral equation that includes fractional integral operators with Mittag-Leffler kernel, many HH-type integral inequalities are derived for the functions whose absolute values of the second derivatives are s-convex and s-concave. Some classical inequalities and hypothesis conditions, such as Hölder’s inequality and Young’s inequality, are taken into account in the proof of the findings.

scholarly journals New Estimations of Hermite–Hadamard Type Integral Inequalities for Special Functions

2021 ◽  
Vol 5 (4) ◽  
pp. 144
Author(s):  
Hijaz Ahmad ◽  
Muhammad Tariq ◽  
Soubhagya Kumar Sahoo ◽  
Jamel Baili ◽  
Clemente Cesarano
Keyword(s):  
Special Functions ◽  
Type Inequality ◽  
Integral Inequalities ◽  
The Novel ◽  
Current Pattern ◽  
Hadamard Inequality ◽  
Special Means ◽  
Algebraic Properties ◽  
Type Integral ◽  
Generalized Integral Inequalities

In this paper, we propose some generalized integral inequalities of the Raina type depicting the Mittag–Leffler function. We introduce and explore the idea of generalized s-type convex function of Raina type. Based on this, we discuss its algebraic properties and establish the novel version of Hermite–Hadamard inequality. Furthermore, to improve our results, we explore two new equalities, and employing these we present some refinements of the Hermite–Hadamard-type inequality. A few remarkable cases are discussed, which can be seen as valuable applications. Applications of some of our presented results to special means are given as well. An endeavor is made to introduce an almost thorough rundown of references concerning the Mittag–Leffler functions and the Raina functions to make the readers acquainted with the current pattern of emerging research in various fields including Mittag–Leffler and Raina type functions. Results established in this paper can be viewed as a significant improvement of previously known results.

scholarly journals On some generalized integral inequalities for Riemann-Liouville fractional integrals

Filomat ◽  
2015 ◽  
Vol 29 (6) ◽  
pp. 1307-1314 ◽  
Author(s):  
Mehmet Sarikaya ◽  
Hatice Filiz ◽  
Mehmet Kiris
Keyword(s):  
Integral Inequalities ◽  
Fractional Integrals ◽  
Generalized Integral Inequalities

scholarly journals Generalized integral inequalities on time scales

2016 ◽  
Vol 2016 (1) ◽  
Author(s):  
Tooba Fayyaz ◽  
Nazia Irshad ◽  
Asif R Khan ◽  
Ghaus ur Rahman ◽  
Gholam Roqia
Keyword(s):  
Time Scales ◽  
Integral Inequalities ◽  
Generalized Integral Inequalities

Some Generalized Integral Inequalities

2011 ◽  
Vol 3 (4) ◽  
pp. 58-66 ◽  
Author(s):  
Dahmani
Keyword(s):  
Integral Inequalities ◽  
Generalized Integral Inequalities
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