Derivatives In Absolute Value Research Articles

Some q-analogues of Hermite–Hadamard inequality of functions of two variables on finite rectangles in the plane

Preliminaries of q-calculus for functions of two variables over finite rectangles in the plane are introduced. Some q-analogues of the famous Hermite–Hadamard inequality of functions of two variables defined on finite rectangles in the plane are presented. A q1q2-Hölder inequality for functions of two variables over finite rectangles is also established to provide some quantum estimates of trapezoidal type inequality of functions of two variables whose q1q2-partial derivatives in absolute value with certain powers satisfy the criteria of convexity on co-ordinates.

Hermite-Hadamard Type Inequalities for convex functions via generalized fractional integral operators

Abstract In this present work, the authors establish a new integral identity involving generalized fractional integral operators and by using this fractional-type integral identity, obtain some new Hermite-Hadamard type inequalities for functions whose first derivatives in absolute value are convex. Relevant connections of the results presented here with those earlier ones are also pointed out.

On generalized Ostrowski-type inequalities for functions whose first derivatives absolute values are convex

In this paper, we establish some generalized Ostrowski-type inequalities for functions whose first derivatives absolute values are convex.

New inequalities of Hermite-Hadamard type for n-times differentiable convex and concave functions with applications

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.

General Lebesgue integral inequalities of Jensen and Ostrowski type for differentiable functions whose derivatives in absolute value are h-convex and applications

Some inequalities related to Jensen and Ostrowski inequalities for general Lebesgue integral of differentiable functions whose derivatives in absolute value are h-convex are obtained. Applications for f-divergence measure are provided as well.

Remarks on some inequalities for s-convex functions and applications

Some new 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.

Some Simpson type integral inequalities for functions whose third derivatives are ( α, m )- GA-convex functions

Abstract By using power-mean integral inequality and Holder’s integral inequality, this paper establishes some new inequalities of Simpson type for functions whose three derivatives in absolute value are the class of (α, m)-geometric-arithmetically-convex functions. Finally, some applications to special means of positive real numbers have also been presented.

Some inequalities for differentiable coordinated convex mappings

In this paper, we indicate some inequalities for double integrals of functions whose partial derivatives in absolute value are convex on the coordinates on rectangle from the plane. Our established results generalize some recent results for functions whose partial derivatives in absolute value are convex on the coordinates on the rectangle from the plane.

On new inequalities of Hermite–Hadamard–Fejér type for convex functions via fractional integrals

In this paper, we establish some weighted fractional inequalities for differentiable mappings whose derivatives in absolute value are convex. These results are connected with the celebrated Hermite–Hadamard–Fejér type integral inequality. The results presented here would provide extensions of those given in earlier works.

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

In this article, a new general identity for continuously twice dierentiable functions is established. By making use of this equality, author has obtained new estimates on generalization of Hermite-Hadamardlike type inequalities for functions whose second derivatives in absolute value at certain powers are convex and concave. Mathematics Subject Classication: 26A33, 26A55, 26D10, 26D15

Inequalities of Hermite-Hadamard-like type for the functions whose second derivatives in absolute value are convex and concave

In this article, new estimates on generalization of Hermite-Hadamardlike type inequalities for functions whose second derivatives in absolute value at certain powers are convex and concave are established. Mathematics Subject Classication: 26D15, 26A51

Hermite-Hadamard-like type inequalities for s-convex functions and s-Godunova-Levin functions of two kinds

In this article, the author establish new estimates on generalization of Hermite-Hadamard-like type inequalities for three times dierentiable functions whose its third derivatives in absolute value at certain powers are convex, s-convex and s-Godunova-Levin functions of two kind, via Riemann-Liouville fractional integrals. Mathematics Subject Classication: 26D15, 26A51

Hermite-Hadamard type inequalities for the functions whose second derivatives in absolute value are convex and concave

Hermite-Hadamard type inequalities for the functions whose second derivatives in absolute value are convex and concave

On some integral inequalities for twice differentiable quasi-convex and convex functions via fractional integrals

In this article, a new general identity for twice dierentiable functions via Riemann-Liouville fractional integrals is established. By making use of this equality, author has obtained new estimates on generalization of Hadamard, Ostrowski and Simpson type inequalities for functions whose second derivatives in absolute value at certain powers are, respectively, convex and quasi-convex functions via Riemann-Liouville fractional integrals.

Generalization of integral inequalities of the type of Hermite-Hadamard through invexity

In this paper, we obtain some inequalities of Hermite-Hadamard type for functions whose derivatives absolute values are prequasiinvex function. Applications to some special means are considered.

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.

On Some Inequalities for Functions Whose Second Derivatives Absolute Values Are S-Geometrically Convex

In this paper, the authors achieve some new Hadamard type in- equalities using elementary well known inequalities for functions whose second derivatives absolute values are s-geometrically and geometrically convex. And also they get some applications for special means for positive numbers.

On Hermite-Hadamard type integral inequalities for functions whose second derivative are nonconvex

In this paper, we extend some estimates of the right hand side of a Hermite- Hadamard type inequality for nonconvex functions whose second derivatives absolute values are $\varphi$-convex, $\log -\varphi$-convex, and quasi- $\varphi$ convex.

Generalization of some inequalities via Riemann-Liouville fractional calculus

Some Hermite-Hadamard type inequalities are provided. We deal with functions whose derivatives in absolute value are convex or concave. By defining two cumulative gaps which enable us to generalize known rezults in the framework of Riemann-Liouville fractional calculus, we open a new perspective on the classic statement of the inequality.