Special Means Of Real Numbers Research Articles

On Hermite-Hadamard Type Inequalities for Functions Whose First Derivative Absolute Values are Convex and Concave

Abstract In this paper, we derive general integral identity by establishing new Hermite-Hadamard type inequalities for functions whose absolute values of derivatives are convex and concave. Cor- responding error estimates for midpoint formula are also included. Moreover, some applications to special means of real numbers are also provided.

Hermite-Hadamard and simpson-like type inequalities for differentiable p-quasi-convex functions

In this paper, we give a new concept which is a generalization of the concepts quasi-convexity and harmonically quasi-convexity and establish a new identity. A consequence of the identity is that we obtain some new general inequalities containing all of the Hermite-Hadamard and Simpson-like type for functions whose derivatives in absolute value at certain power are p-quasi-convex. Some applications to special means of real numbers are also given.

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

AbstractWe 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

Fractional Hermite-Hadmard inequalities for convex functions and applications

In this paper, we derive a new lemma including third-order derivative of a function via fractional integrals. Using this lemma, we establish some new fractional estimates for Hermite-Hadamard type inequalities for convex functions. Several special cases are also discussed. Some applications to special means of real numbers are also discussed. The ideas and techniques used in this paper may stimulate future investigations regarding Hermite-Hadamard type of inequalities and its application in different areas.

Parametrized inequality of Hermite-Hadamard type for functions whose third derivative absolute values are quasi-convex.

In this paper we present some inequalities of Hermite-Hadamard type for functions whose third derivative absolute values are quasi-convex. Moreover, an application to special means of real numbers is also considered.

Some new inequalities of Hermite-Hadamard type for $s$-convex functions

Some new results related of the left-hand side of the Hermite-Hadamard type inequal- ities for the class of mappings whose second derivatives at certain powers are s convex in the second sense are established. Also, some applications to special means of real numbers are provided. 2010 Mathematics Subject Classification: 26A51; 26D07; 26D10; 26D15

Some new general integral inequalities for P-functions

In this paper, we derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in absolute value at certain power are P-functions. Some applications to special means of real numbers are also given.

On new general integral inequalities for s-convex functions

In this paper, the authors establish some new estimates for the remainder term of the midpoint, trapezoid, and Simpson formula using functions whose derivatives in absolute value at certain power are s-convex. Some applications to special means of real numbers are provided as well.

Hermite-Hadamard and Simpson Type Inequalities for Differentiable P-GA-Functions

The author introduces the concept of the P-GA-functions, gives Hermite-Hadamard's inequalities for P-GA-functions, and defines a new identity. By using this identity, the author obtains new estimates on generalization of Hadamard and Simpson type inequalities for P-GA-functions. Some applications to special means of real numbers are also given.

Inequalities of Hermite–Hadamard type for functions whose derivatives in absolute value are convex with applications

In this paper some new Hadamard-type inequalities for functions whose derivatives in absolute values are convex are established. Some applications to special means of real numbers are given. Finally, we also give some applications of our obtained results to get new error bounds for the sum of the midpoint and trapezoidal formulae.

Applying GG-Convex Function to Hermite-Hadamard Inequalities Involving Hadamard Fractional Integrals

By virtue of fractional integral identities, incomplete beta function, useful series, and inequalities, we apply the concept of GG-convex function to derive new type Hermite-Hadamard inequalities involving Hadamard fractional integrals. Finally, some applications to special means of real numbers are demonstrated.

Hermite-Hadamard and Simpson-Like Type Inequalities for Differentiable Harmonically Convex Functions

A new identity for differentiable functions is derived. A consequence of the identity is that the author establishes some new general inequalities containing all of the Hermite-Hadamard and Simpson-like types for functions whose derivatives in absolute value at certain power are harmonically convex. Some applications to special means of real numbers are also given.

On New Integral Inequalities with Applications

On New Integral Inequalities with Applications Ugur S. Kirmaci Abstract We present several general integral inequalities for convex and concave mappings. Some new inequalities of the Simpson’s type and the Hermite-Hadamard’s type are obtained. Finally, some applications to special means of real numbers are also given. Full Text: PDF DOI: 10.15640/arms.v2n2a6

Refinements of Hermite-Hadamard Type Inequalities Involving Fractional Integrals

In this paper, Hermite-Hadamard type inequalities involving Hadamard fractional integrals via convex functions are studied. An important integral identity and new Hermite-Hadamard type integral inequalities involving Hadamard fractional integrals are also presented. Some applications to special means of real numbers are given.

NEW ESTIMATES ON GENERALIZATION OF SOME INTEGRAL INEQUALITIES FOR s-CONVEX FUNCTIONS AND THEIR APPLICATIONS

In this paper, a new identity for differentiable functions is derived. Thus we can obtain new estimates on generalization of Hadamard,Ostrowski and Simpson type inequalities for functions whose derivatives in absolute value at certain power are s-convex (in the second sense). Some applications to special means of real numbers are also given.

On some inequalities for s-convex functions and applications

Abstract Some new results related to the left-hand side of the Hermite-Hadamard type inequalities for the class of functions whose second derivatives at certain powers are s-convex functions in the second sense are obtained. Also, some applications to special means of real numbers are provided. MSC:26A51, 26D15.

New generalized Hermite-Hadamard type inequalities and applications to special means

In this paper, Hermite-Hadamard type inequalities involving Hadamard fractional integrals for the functions satisfying monotonicity, convexity and s-e-condition are studied. Three classes of left-type Hadamard fractional integral identities including the first-order derivative are firstly established. Some interesting Hermite-Hadamard type integral inequalities involving Hadamard fractional integrals are also presented by using the established integral identities. Finally, some applications to special means of real numbers are given. MSC: 26A33; 26A51; 26D15

New inequalities for Hermite-Hadamard and Simpson type with applications

In this paper, we obtain new bounds for the inequalities of Simpson and Hermite-Hadamard type for functions whose second derivatives absolute values are $P$-convex. Some applications for special means of real numbers are also given.

On New Inequalities of Simpson’s Type for Functions Whose Second Derivatives Absolute Values are Convex

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.

A generalizations of Simpson’s type inequality for differentiable functions using ( α , m ) -convex functions and applications

In this paper, we establish some new inequalities of Simpson’s type based on -convexity for differentiable mappings. This contributes to new better estimates than presented already. Some applications for special means of real numbers and error estimates for some numerical quadrature rules are also given. MSC:26D15, 26D10.