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In the paper, the authors correct the paper "Mevlüt Tunç, On some integral inequalities for s-geometrically convex functions and their applications, Int. J. Open Problems Comput. Math. 6 (2013), no. 1, 53-63; available online at http://dx.doi.org/10.12816/0006155." [ABSTRACT FROM AUTHOR]

In the paper, by virtue of an integral identity and the Hölder inequality for integrals, the authors establish some new inequalities of the Hermite-Hadamard type for -convex functions, derive some new inequalities of common convex functions, and apply these new results to construct some inequalities for special means. [ABSTRACT FROM AUTHOR]

In the paper, by establishing a Riemann-Liouville fractional integral identity involving an n-times differentiable function, the authors present some Hermite-Hadamard type inequalities involving Riemann-Liouville fractional integrals for s-convex functions. [ABSTRACT FROM AUTHOR]

In this paper, the authors introduce a notion "(α, m)-GA-convex function" and establish some Hermite-Hadamard type inequalities for this kind of convex functions. [ABSTRACT FROM AUTHOR]

In the paper, the authors define the concepts of (α,m)-harmonic-arithmetically convex functions and strongly (α,m)-harmonic-arithmetically convex functions, establish a new integral identity, and present some new Hermite-Hadamard type inequalities for (α,m)-harmonic-arithmetically convex functions and strongly (α,m)-harmonic-arithmetically convex functions. [ABSTRACT FROM AUTHOR]

In the paper, the authors establish some integral inequalities of extended Simpson type for (α,m)-ε-convex functions. [ABSTRACT FROM AUTHOR]

In this paper, we establish some integral inequalities of Simpson's type for (α,m)-convex functions. [ABSTRACT FROM AUTHOR]

In the paper, the authors establish some new integral inequalities for log-convex functions on co-ordinates. These newly-established inequalities are connected with integral inequalities of the Hermite-Hadamard type for log-convex functions on co-ordinates. [ABSTRACT FROM AUTHOR]

In the paper, the authors find two sharp and double inequalities for bounding the second Seiffert mean either by a one-parameter family of means derived from the centroidal mean or by a convex combination of the arithmetic and contra-harmonic means. [ABSTRACT FROM AUTHOR]

In the paper, the authors introduce a new concept geometrically mean convex function on co-ordinates and establish some new integral inequalities of Hermite-Hadamard type for geometrically mean convex functions of two variables on the co-ordinates. [ABSTRACT FROM AUTHOR]

In the paper, the authors introduce a new concept "(log, (α,m))-convex functions on the co-ordinates on the rectangle of the plane" and establish some new integral inequalities of Hermite-Hadamard type for (log, (α,m))-convex functions on the co-ordinates on the rectangle from the plane. [ABSTRACT FROM AUTHOR]

In the paper, the authors establish some new inequalities of Simpson type for functions whose third derivatives are extended s-convex functions, and apply these inequalities to derive some inequalities of special means. [ABSTRACT FROM AUTHOR]

Some new integral inequalities of Hermite-Hadamard type for the product of strongly logarithmically convex functions and other convex functions such as the P-convex, quasi-convex, m-convex, (α,m)-convex and s-convex functions have been established. [ABSTRACT FROM AUTHOR]

In the paper, the authors establish some Hermite-Hadamard type inequalities for the product of two (α, m)-convex functions. [ABSTRACT FROM AUTHOR]

In the paper, by creating an integral identity involving an n-times differentiable function, the authors establish some new Hermite-Hadamard type inequalities for preinvex functions and generalize some known results. [ABSTRACT FROM AUTHOR]

In the paper, some new inequalities of Hermite-Hadamard type for (α, m)-convex functions are obtained. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The authors introduce the concept of the s-geometrically convex functions. By the well-known Hölder inequality, they establish some integral inequalities of Hermite-Hadamard type related to the s-geometrically convex functions and apply these inequalities to special means. [ABSTRACT FROM AUTHOR]

Let a and b be two real numbers and f be a positive and differentiable function on an interval I. The authors establish the i-log-convex or i-log-concave properties for i∈ of the function [f(bx)]a/[f(ax)]b for ax∈I and bx∈I when the function uk-1[ln f(u)](k) for k∈ is monotonic and apply these properties to deduce some known and new conclusions related to some special functions, such as the gamma function, Riemann's zeta function, complete elliptic integrals, exponential mean, and extended mean values. [ABSTRACT FROM AUTHOR]

In the paper, the authors introduce a new concept "strongly extended (s,m)-convex function" and establish some integral inequalities of Simpson's type for strongly extended (s,m)- convex functions. [ABSTRACT FROM AUTHOR]

In the paper, the authors introduce a notion "(α, m)-GA-convex functions" and establish some integral inequalities of Hermite-Hadamard type for (α, m)-GA-convex functions. 2010 Mathematics Subject Classification: Primary 26A51; Secondary 26D15, 26E60, 41A55. [ABSTRACT FROM AUTHOR]

In the paper, the authors introduce a notion "(α,m)-GA-convex functions" and establish some integral inequalities of Hermite-Hadamard type for (α,m)-GA-convex functions. [ABSTRACT FROM AUTHOR]

In the paper, the authors establish a new integral identity and, by this identity and Hölder's inequality, discover some new Hermite-Hadamard type integral inequalities for functions whose third derivatives are (α, m)-convex. [ABSTRACT FROM AUTHOR]