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 New Hermite Hadamard type inequalities for twice differentiable convex mappings via Green function and applications

2016 ◽  
Vol 2 (2) ◽  
pp. 107-118 ◽  
Author(s):  
Samet Erden ◽  
Mehmet Zeki Sarikaya
Keyword(s):  
Green Function ◽  
Integral Inequalities ◽  
Real Numbers ◽  
Absolute Value ◽  
Convex Mappings ◽  
Trapezoidal Formula ◽  
Special Means ◽  
Second Derivatives ◽  
Type Integral

Abstract We derive some Hermite Hamamard type integral inequalities for functions whose second derivatives absolute value are convex. Some eror estimates for the trapezoidal formula are obtained. Finally, some natural applications to special means of real numbers are given

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 Fractional Ostrowski type inequalities for differentiable harmonically convex functions

2021 ◽  
Vol 7 (3) ◽  
pp. 3939-3958
Author(s):  
Thanin Sitthiwirattham ◽  
◽  
Muhammad Aamir Ali ◽  
Hüseyin Budak ◽  
Sotiris K. Ntouyas ◽  
...  
Keyword(s):  
Convex Functions ◽  
Fractional Integrals ◽  
Real Numbers ◽  
Special Means ◽  
Special Cases ◽  
Harmonically Convex Functions ◽  
New Inequalities

<abstract><p>In this paper, we prove some new Ostrowski type inequalities for differentiable harmonically convex functions using generalized fractional integrals. Since we are using generalized fractional integrals to establish these inequalities, therefore we obtain some new inequalities of Ostrowski type for Riemann-Liouville fractional integrals and $ k $-Riemann-Liouville fractional integrals in special cases. Finally, we give some applications to special means of real numbers for newly established inequalities.</p></abstract>

scholarly journals Some new inequalities for convex functions via generalized integral operators and their applications

Mathematica ◽  
2021 ◽  
Vol 63 (86) (2) ◽  
pp. 268-283
Author(s):  
Artion Kashuri ◽  
◽  
Themistocles M. Rassias ◽  
Keyword(s):  
Integral Equation ◽  
Integral Operator ◽  
Error Estimates ◽  
Integral Inequality ◽  
Convex Functions ◽  
Integral Operators ◽  
Absolute Value ◽  
Special Means ◽  
Type Integral ◽  
New Inequalities

The authors discover an identity for a generalized integral operator via differentiable function. By using this integral equation, we derive some new bounds on Hermite–Hadamard type integral inequality for differentiable mappings that are in absolute value at certain powers convex. Our results include several new and known results as particular cases. At the end, some applications of presented results for special means and error estimates for the mixed trapezium and midpoint formula have been analyzed. The ideas and techniques of this paper may stimulate further research in the field of integral inequalities.

scholarly journals Some new inequalities of Hermite-Hadamard type for s-convex functions with applications

2017 ◽  
Vol 15 (1) ◽  
pp. 1414-1430 ◽  
Author(s):  
Muhammad Adil Khan ◽  
Yuming Chu ◽  
Tahir Ullah Khan ◽  
Jamroz Khan
Keyword(s):  
Convex Functions ◽  
Fractional Integrals ◽  
Concave Functions ◽  
Trapezoidal Formula ◽  
Error Estimations ◽  
New Inequalities

Abstract In this paper, we present several new and generalized Hermite-Hadamard type inequalities for s-convex as well as s-concave functions via classical and Riemann-Liouville fractional integrals. As applications, we provide new error estimations for the trapezoidal formula.

scholarly journals Inequalities via s−convexity and log −convexity

2017 ◽  
Vol 5 (1) ◽  
pp. 74-85
Author(s):  
Ahmet Ocak Akdemir ◽  
Merve Avcı Ardıç ◽  
M. Emin Özdemir
Keyword(s):  
Numerical Integration ◽  
Absolute Value ◽  
Second Derivatives ◽  
New Inequalities

AbstractIn this paper, we obtain some new inequalities for functions whose second derivatives’ absolute value is s−convex and log −convex. Also, we give some applications for numerical integration.

scholarly journals HERMITE–HADAMARD TYPE INEQUALITIES FOR FUNCTIONS WHEN A POWER OF THE ABSOLUTE VALUE OF THE FIRST DERIVATIVE IS P-CONVEX

2011 ◽  
Vol 86 (1) ◽  
pp. 126-134 ◽  
Author(s):  
A. BARANI ◽  
S. BARANI
Keyword(s):  
Type Inequality ◽  
Absolute Value ◽  
Trapezoidal Formula ◽  
First Derivative ◽  
Right Hand ◽  
Special Means ◽  
The Absolute ◽  
The Right

AbstractIn this paper we extend some estimates of the right-hand side of a Hermite–Hadamard type inequality for functions whose derivatives’ absolute values are P-convex. Applications to the trapezoidal formula and special means are introduced.

scholarly journals New inequalities of Hermite-Hadamard type for functions whose second derivatives absolute values are quasi-convex

2010 ◽  
Vol 41 (4) ◽  
pp. 353-359 ◽  
Author(s):  
Mohammad W Alomari ◽  
Maslina Darus ◽  
Sever S. Dragomir
Keyword(s):  
Special Means ◽  
Second Derivatives ◽  
New Inequalities

In this note we obtain some inequalities of Hermite-Hadamardtype for functions whose second derivatives absolute values are quasi-convex.Applications for special means are also provided.

scholarly journals Some New Inequalities on Generalization of Hermite-Hadamard and Bullen Type Inequalities, Applications to Trapezoidal and Midpoint Formula

2021 ◽  
Vol 45 (4) ◽  
pp. 647-657
Author(s):  
İMDAT İŞCAN ◽  
◽  
TEKİN TOPLU ◽  
FATİH YETGİN ◽  
◽  
...  
Keyword(s):  
Error Estimates ◽  
Real Numbers ◽  
Absolute Value ◽  
General Identity ◽  
Differentiable Functions ◽  
Special Means ◽  
New Inequalities

In this paper, we give a new general identity for differentiable functions. A consequence of the identity is that we obtain some new general inequalities containing all of the Hermite-Hadamard and Bullen type for functions whose derivatives in absolute value at certain power are convex. Some applications to special means of real numbers are also given. Finally, some error estimates for the trapezoidal and midpoint formula are addressed.

Sign in / Sign up

Export Citation Format

Share Document