New Inequalities Of Hermite-Hadamard Type Research Articles

Hermite-Hadamard type integral inequalities for geometric-arithmetically (s,m) convex functions

In this paper, we introduce a definition of geometric-arithmetically \((s,m)\) convex function and give some new inequalities of Hermite-Hadamard type for the geometric-arithmetically \((s,m)\) convex function. Finally, we discuss applications of these inequalities to special means.

New inequalities of hermite-hadamard type for functions whose second derivatives absolute values are exponential trigonometric convex

New inequalities of hermite-hadamard type for functions whose second derivatives absolute values are exponential trigonometric convex

New inequalities of Hermite-Hadamard type for h-convex functions via generalized fractional integrals

New inequalities of Hermite-Hadamard type for h-convex functions via generalized fractional integrals

On some new fractional Hermite-Hadamard type inequalities for convex and co-ordinated convex functions

In this study, some new inequalities of Hermite-Hadamard type for convex and co-ordinated convex functions via Riemann-Liouville fractional integrals are derived. It is also shown that the results obtained in this paper are the extension of some earlier ones.

New integral inequalities for differentiable convex functions via Atangana-Baleanu fractional integral operators

• Contain interesting results linking fractional analysis and inequality theory. • Hadamard type results in inequality theory for the Atangana-Baleanu integral operator. • New approaches and bounds for Hadamard-type inequalities. • New and motivated inequalities derived from the help of Jensen, Hólder and Young inequalities. Inequalities, including fractional integrals, have become a very popular method and have been the main motivation point for many studies in recent years. Studies have been carried out for many types of inequality, thereby introducing a new trend in inequality theory. In this study, new inequalities of Hermite-Hadamard type were obtained by using Atangana-Baleanu integral operators, which provide very useful and effective results with their use in fields such as fractional analysis, applied mathematics, mathematical biology and engineering. The fact that the main results were obtained for functions whose absolute value of the second derivative is convex. In the study, we have proved a new identity for twice differentiable convex functions and the modified version of the integral identity was given in the last section.

Hermite-Hadamard Type Inequalities for Exponentially p-Convex Stochastic Processes

In this paper, the concept of exponentially 𝑝-convex stochastic process is introduced. Several new inequalities of Hermite-Hadamard type for exponentially 𝑝-convex stochastic process are established. Some special cases are given which are obtained from our main results. The results obtained in this work are the generalizations of the known results.

Hermite-Hadamard Type Inequalities for m-Convex and (α, m)-Convex Stochastic Processes

In this paper, the concepts of m-convex and (α, m)-convex stochastic processes are introduced. Several new inequalities of Hermite-Hadamard type for differentiable m-convex and (α, m)-convex stochastic processes are established. The results obtained in this work are the generalizations of the known results.

New inequalities of Hermite-Hadamard type for HA-convex functions

Some new inequalities of Hermite-Hadamard type for HA-convex functions defined on positive intervals are given.

Some new inequalities of Hermite-Hadamard type for GA-convex functions

Some new inequalities of Hermite-Hadamard type for GA-convex functions defined on positive intervals are given. Refinements and weighted version of known inequalities are provided. Some applications for special means are also obtained.

New weighted inequalities for higher order derivatives and applications

We establish a new Ostrowski type inequality for (n+1)-times differentiable mappings which are bounded. Then, some new inequalities of Hermite-Hadamard type are obtained for functions whose (n+1) th derivatives in absolute value are convex. Spacial cases of these inequalities reduce some well known inequalities. With the help of obtained inequalities, we give applications for the kth-moment of random variables.

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

Abstract In this paper, we present several new and generalized Hermite-Hadamard type inequalities for s-convex as well as s-concave functions via classical and Riemann-Liouville fractional integrals. As applications, we provide new error estimations for the trapezoidal formula.

Inequalities of Hermite-Hadamard Type for HA-Convex Functions

AbstractSome new inequalities of Hermite-Hadamard type for HA-convex functions defined on positive intervals are given.

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.

Integral Inequalities for Some New Classes of Convex Functions

In this paper, we introduce a new class of convex functions, which is called nonconvex functions. We show that this class unifies several previously known and new classes of convex functions. We derive several new inequalities of Hermite-Hadamard type for nonconvex functions. Some special cases are also discussed. Results proved in this paper continue to hold for these special cases.

Generalized Convexity and Integral Inequalities

In this paper, we consider a very useful and significant class of convex sets and convex functions that is relative convex sets and relative convex functions which was introduced and studied by Noor (20). Several new inequalities of Hermite-Hadamard type for relative convex functions are established using different approaches. We also introduce relative h-convex functions and is shown that relative h-convex functions include Noor relative convex functions as special cases. Results obtained in this paper may inspire f uture research in convex analysis and related optimization fields .

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

Hermite-Hadamard Type Inequalities for (<i>m, h</i><SUB><i>1</i></SUB><i>, h</i><SUB><i>2</i></SUB>)-Convex Functions Via Riemann-Liouville Fractional Integrals

In the paper, via Riemann-Liouville fractional integration, the authors present some new inequalities of Hermite-Hadamard type for functions whose derivatives in absolute value are (<i>m, h</i><SUB><i>1</i></SUB><i>, h</i><SUB><i>2</i></SUB>)-convex.

Some New Inequalities of Hermite-Hadamard Type for (α1,m1)-(α2,m2)-Convex Functions on Coordinates

The author introduces a new concept “(α1,m1)-(α2,m2)-convex functions on coordinates” and establishes some new inequalities of Hermite-Hadamard type for (α1,m1)-(α2,m2)-convex functions of two variables on co-ordinates.

Integral inequalities of Hermite-Hadamard type for functions whose third derivatives are convex

In the paper, the authors establish some new inequalities of Hermite-Hadamard type for functions whose third derivatives are convex. MSC: 26D15, 26A51, 41A55.

On new inequalities of Hermite-Hadamard type for functions whose third derivative absolute values are quasi-convex with applications

We establish some new inequalities of Hermite-Hadamard type for functions whose third derivatives absolute values are quasi-convex. Applications to special means have also been presented.