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

2014 ◽  
Vol 8 ◽  
pp. 777-791
Author(s):  
Jaekeun Park
Keyword(s):  
Absolute Value ◽  
Second Derivatives ◽  
New Inequalities

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 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 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 Some new Ostrowski and Gr"Uss type inequalities

2007 ◽  
Vol 38 (2) ◽  
pp. 111-120 ◽  
Author(s):  
B. G. Pachpatte
Keyword(s):  
Differentiable Functions ◽  
Second Derivatives ◽  
Integral Identities ◽  
New Inequalities

In this paper we establish some new inequalities of Ostrowski and Gr"uss type, involving three functions whose second derivatives are bounded. The analysis used in the proofs is fairly elementary and based on the integral identities for twice differentiable functions.

scholarly journals Quantum Hermite–Hadamard-type inequalities for functions with convex absolute values of second $q^{b}$-derivatives

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Muhammad Aamir Ali ◽  
Hüseyin Budak ◽  
Mujahid Abbas ◽  
Yu-Ming Chu
Keyword(s):  
Convex Functions ◽  
Differentiable Functions ◽  
Right Hand ◽  
Second Derivatives ◽  
New Inequalities

AbstractIn this paper, we obtain Hermite–Hadamard-type inequalities of convex functions by applying the notion of $q^{b}$ q b -integral. We prove some new inequalities related with right-hand sides of $q^{b}$ q b -Hermite–Hadamard inequalities for differentiable functions with convex absolute values of second derivatives. The results presented in this paper are a unification and generalization of the comparable results in the literature on Hermite–Hadamard inequalities.

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