Hermite-Hadamard Integral Inequalities Research Articles

A discrete/continuous choice model on a nonconvex budget set

ABSTRACTDecreasing block rate pricing is a nonlinear price system often used for public utility services. Residential gas services in Japan and the United Kingdom are provided under this price schedule. The discrete/continuous choice approach is used to analyze the demand under decreasing block rate pricing. However, the nonlinearity problem, which has not been examined in previous studies, arises because a consumer’s budget set (a set of affordable consumption amounts) is nonconvex, and hence, the resulting model includes highly nonlinear functions. To address this problem, we propose a feasible, efficient method of demand estimation on the nonconvex budget. The advantages of our method are as follows: (i) the construction of an Markov chain Monte Carlo algorithm with an efficient blanket based on the Hermite–Hadamard integral inequality and the power-mean inequality, (ii) the explicit consideration of the (highly nonlinear) separability condition, which often makes numerical likelihood maximization difficult, and (iii) the introduction of normal disturbance into the discrete/continuous choice model on the nonconvex budget set. The proposed method is applied to estimate the Japanese residential gas demand function and evaluate the effect of price schedule changes as a policy experiment.

A note on geometrically convex functions

Abstract In this paper, we establish several new inequalities for twice differentiable mappings that are connected with the celebrated Hermite-Hadamard integral inequality. MSC:26D15, 26A51.

Some Results on Hermite-Hadamard Type Inequality through Convexity

Our aim in this article to establish various inequalities for some differentiable mapping that are connected with illustrious Hermite-Hadamard integral inequality for mapping whose absolute values of derivatives are convex. The new integral inequalities are then applied to some special means and as well as numerical integration to obtain some better estimates.

Some inequalities for differentiable convex mapping with application to weighted midpoint formula and higher moments of random variables

Connected with the celebrated Hermite–Hadamard integral inequality, several new inequalities for differentiable convex, wright-convex and quasi-convex mapping are established. Applications of these results are considered in error estimates for weighted Midpoint integral formula and in deriving the inequalities involving higher moments of random variables.

GENERALISATIONS OF INTEGRAL INEQUALITIES OF HERMITE–HADAMARD TYPE THROUGH CONVEXITY

AbstractIn this paper, we establish various inequalities for some differentiable mappings that are linked with the illustrious Hermite–Hadamard integral inequality for mappings whose derivatives are $s$-$(\alpha , m)$-convex. The generalised integral inequalities contribute better estimates than some already presented. The inequalities are then applied to numerical integration and some special means.

Some Hermite-Hadamard type inequalities for n-time differentiable "Equation missing" -convex functions

Abstract In the paper, the famous Hermite-Hadamard integral inequality for convex functions is generalized to and refined as inequalities for n-time differentiable functions which are ( α , m ) -convex. MSC: 26D15, 26A51, 41A55.

New Inequalities of Hermite-Hadamard Type for Functions Whose Second Derivatives Absolute Values Are Convex and Quasi-Convex

In this paper, we establish several new inequalities for twice differantiable mappings that are connected with the celebrated Hermite-Hadamard integral inequality. Some applications for special means of real numbers are also provided.

Generalizations of Hermite–Hadamard inequality ton-time differentiable functions which ares-convex in the second sense

In the paper, the famous Hermite–Hadamard integral inequality for convex functions is generalized to and refined as the ones for n -time differentiable functions which are s -convex in the second sense, and some known results are improved.

On the refinements of the Hermite-Hadamard inequality

In this paper, we present some refinements of the classical Hermite-Hadamard integral inequality for convex functions. Further, we give the concept of n-exponential convexity and log-convexity of the functions associated with the linear functionals defined by these inequalities and prove monotonicity property of the generalized Cauchy means obtained via these functionals. Finally, we give several examples of the families of functions for which the results can be applied.MSC: 26D15.

Some new bounds for two mappings related to the Hermite-Hadamard inequality for convex functions

Some new results concerning two mappings associated to the celebrated Hermite-Hadamard integral inequality for convex function with applications for special means are given.

Some Integral Inequalities of Hermite-Hadamard Type for Convex Functions with Applications to Means

The authors establish some new inequalities for differentiable convex functions, which are similar to the celebrated Hermite-Hadamard's integral inequality for convex functions, and apply these inequalities to construct inequalities for special means of two positive numbers.

Some inequalities for differentiable convex mapping with application to weighted trapezoidal formula and higher moments of random variables

Several inequalities for differentiable convex, wright-convex and quasi-convex mapping are obtained respectively that are connected with the celebrated Hermite–Hadamard integral inequality. Also, some error estimates for weighted Trapezoid formula and higher moments of random variables are given.

Some New Inequalities of Hermite-Hadamard's Type

In this paper, we establish several new inequalities for some differantiable mappings that are connected with the celebrated Hermite-Hadamard integral inequality. Some applications for special means of real numbers are also provided.

On Minkowski and Hermite-Hadamard integral inequalities via fractional integration

In this paper, we use the the Riemann-Liouville fractional integral to develop some new results related to the Hermite-Hadamard inequality. Other integral inequalities related to the Minkowsky inequality are also established. Our results have some relationships with [E. Set, M. E. Ozdemir and S.S. Dragomir, J. Inequal. Appl. 2010, Art. ID 148102, 9 pp.] and [L. BougoffaJ. qualPure and ApplMath 7 (2006), no. 2, Article 60, 3 pp.]. Some interested inequalities of these references can be deduced as some special cases.

WITHDRAWN: On Hermite–Hadamard integral inequalities involving two preinvex functions

WITHDRAWN: On Hermite–Hadamard integral inequalities involving two preinvex functions

Improvement and further generalization of inequalities for differentiable mappings and applications

Based on the celebrated Hermite–Hadamard integral inequality for convex functions, some inequalities for differentiable convex and concave mappings are generalized. Furthermore, the results obtained are examined in the context of special means for real numbers.

A Sequence of Mappings Associated with the Hermite-Hadamard Inequalities and Applications

New properties for some sequences of functions defined by multiple integrals associated with the Hermite-Hadamard integral inequality for convex functions and some applications are given.

Some inequalities for differentiable convex and concave mappings

Several inequalities are obtained for some differentiable convex mappings that are connected with the celebrated Hermite-Hadamard integral inequality. Also a parallel development is made for concave functions.

On some inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula

Some inequalities are presented here for differentiable convex mappings, using Hermite–Hadamard's integral inequality holding for convex functions. A parallel development is deduced for differentiable concave functions. Some applications to special means of real numbers are also given. Finally, some error estimates for the midpoint formula are obtained.

Further properties of some mappings associated with Hermite-Hadamard inequalities

New properties of some functionals associated to the Hermite-Hadamard integral inequality for convex functions are given.