Some inequalities of Hermite-Hadamard-like type for the functions whose second derivatives in absolute value are convex

2015 ◽  
Vol 9 ◽  
pp. 3071-3086
Author(s):  
Jaekeun Park
Keyword(s):  
Absolute Value ◽  
Second Derivatives

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 version of fractional Simpson type inequalities for twice differentiable functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Fatih Hezenci ◽  
Hüseyin Budak ◽  
Hasan Kara
Keyword(s):  
Present Article ◽  
Convex Functions ◽  
Absolute Value ◽  
Differentiable Functions ◽  
Second Derivatives

AbstractSimpson inequalities for differentiable convex functions and their fractional versions have been studied extensively. Simpson type inequalities for twice differentiable functions are also investigated. More precisely, Budak et al. established the first result on fractional Simpson inequality for twice differentiable functions. In the present article, we prove a new identity for twice differentiable functions. In addition to this, we establish several fractional Simpson type inequalities for functions whose second derivatives in absolute value are convex. This paper is a new version of fractional Simpson type inequalities for twice differentiable functions.

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 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 Some Ostrowski’S Type Inequalities For Functions Whose Second Derivatives Are S-Convex In The Second Sense

2014 ◽  
Vol 47 (1) ◽  
Author(s):  
Erhan Set ◽  
Mehmet Zeki Sarikaya, ◽  
M. Emin Ozdemir
Keyword(s):  
Absolute Value ◽  
Second Derivatives ◽  
New Inequalities ◽  
Differentiable Mappings

AbstractSome new inequalities of the Ostrowski type for twice differentiable mappings whose derivatives in absolute value are s-convex in the second sense are given

scholarly journals New Simpson type inequalities for twice differentiable functions via generalized fractional integrals

2021 ◽  
Vol 7 (3) ◽  
pp. 3959-3971
Author(s):  
Xuexiao You ◽  
◽  
Fatih Hezenci ◽  
Hüseyin Budak ◽  
Hasan Kara ◽  
...  
Keyword(s):  
Convex Functions ◽  
Fractional Integrals ◽  
Absolute Value ◽  
Differentiable Functions ◽  
Second Derivatives

<abstract><p>Fractional versions of Simpson inequalities for differentiable convex functions are extensively researched. However, Simpson type inequalities for twice differentiable functions are also investigated slightly. Hence, we establish a new identity for twice differentiable functions. Furthermore, by utilizing generalized fractional integrals, we prove several Simpson type inequalities for functions whose second derivatives in absolute value are convex.</p></abstract>

scholarly journals Hermite-Hadamard type inequalities for twice differantiable functions via generalized fractional integrals

Filomat ◽  
2019 ◽  
Vol 33 (15) ◽  
pp. 4967-4979
Author(s):  
Hüseyin Budak ◽  
Fatma Ertuğral ◽  
Ebru Pehlivan
Keyword(s):  
Fractional Integrals ◽  
Absolute Value ◽  
Second Derivatives ◽  
Differentiable Mappings

In this paper we first obtain two generalized identities for twice differentiable mappings involving generalized fractional integrals defined by Sarikaya and Ertu?ral. Then we establish some midpoint and trapezoid type inequalities for functions whose second derivatives in absolute value are convex.

scholarly journals More on Ostrowski Type Inequalities for some S-Convex Functions in the Second Sense

2016 ◽  
Vol 49 (4) ◽  
Author(s):  
Zeng Liu
Keyword(s):  
Convex Functions ◽  
Absolute Value ◽  
Second Derivatives ◽  
Published Paper

AbstractSome Ostrowski type inequalities for functions whose second derivatives in absolute value at certain powers are s-convex in the second sense are established. Two mistakes in a recently published paper are pointed out and corrected.

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