Derivatives In Absolute Value Research Articles

GENERALIZED n-POLYNOMIAL P-FUNCTIONS WITH SOME RELATED INEQUALITIES AND THEIR APPLICATIONS

Abstract. In this paper, we introduce the notion of generalized n-polynomial P-function. We explore some algebraic properties of this function class. Additionally, we establish a new trapezium type inequality for this generalized class of functions and derive several refinements of the trapezium type inequality for functions whose first derivative in absolute value at a certain power is generalized n-polynomial P-function. Finally, we conclude our paper by exploring some applications of the results we have obtained in the context of special means. Our novel findings generalize previously known results in the literature.

On strongly m-convex stochastic processes

AbstractIn this paper, we introduce the concept of strongly m-convex stochastic processes and present some basic properties of these stochastic processes. We derive Hermite-Hadamard type inequalities for stochastic processes whose first derivatives in absolute values are strongly m-convex. The results presented in this paper are a generalization and extension of previously known results.

Simpson Type Estimations for Convex Functions via Quantum Calculus

We first establish a new identity including quantum integrals and quantum numbers via q -differentiable functions. After that, with the help of this equality, a Simpson-type inequality for functions whose quantum derivatives in modulus are convex is derived, and some new inequalities for powers of quantum derivatives in absolute value are provided. It is also discussed how results come out in the case when q approaches 1. Mathematics Subject Classification: 26D15, 26D10, 26A51, 34A08.

New Weighted Inequalities for Functions Whose Higher-Order Partial Derivatives Are Co-Ordinated Convex

The purpose of this study is to establish recent inequalities based on double integrals of mappings whose higher-order partial derivatives in absolute value are convex on the co-ordinates on rectangle from the plane. Also, some special cases of results improved in this study are examined.

Better Approximations for Quasi-Convex Functions

In this paper, by using Hölder-İşcan, Hölder integral inequality and a general identity for differentiable functions we can get new estimates on generalization of Hadamard, Ostrowski and Simpson type integral inequalities for functions whose derivatives in absolute value at certain power are quasi-convex functions. It is proved that the result obtained Hölder-İşcan integral inequality is better than the result obtained Hölder inequality. Keywords: Hölder-İşcan scan inequality, Hermite-Hadamard inequality, Simpson and Ostrowski type inequality, midpoint and trapezoid type inequality, quasi-convex functions.

Ostrowski Type Inequalities Via ψ − (α, β, γ, δ)−Convex Function

In this paper, we are introducing very first time the class of ψ − (α, β, γ, δ)−convex function in mixed kind, which is the generalization of many classes of convex functions. We would like to state well-known Ostrowski inequality via Montgomery identity for ψ−(α, β, γ, δ)−convex function in mixed kind. In addition, we establish some Ostrowski type inequalities for the class of functions whose derivatives in absolute values at certain powers are ψ − (α, β, γ, δ)-convex functions in mixed kind by using different techniques including Hölder's inequality and power mean inequality. Also, various established results would be captured as special cases. Moreover, some applications in terms of special means would also be given. Keywords: Ostrowski inequality, Montgomery identity, convex functions, special means.

Generalized n-Polynomial p-Convexity and Related Inequalities

In this paper, we construct a new class of convex functions, so-called generalized n-polynomial p-convex functions. We investigate their algebraic properties and provide some relationships between these functions and other types of convex functions. We establish Hermite–Hadamard (H–H) inequality for the newly defined class of functions. Additionally, we derive refinements of H–H inequality for functions whose first derivatives in absolute value at certain power are generalized n-polynomial p-convex. When p=−1, our definition evolves into a new definition for the class of convex functions so-called generalized n-polynomial harmonically convex functions. The results obtained in this study generalize regarding those found in the existing literature. By extending these particular types of inequalities, the objective is to unveil fresh mathematical perspectives, attributes and connections that can enhance the evolution of more resilient mathematical methodologies. This study aids in the progression of mathematical instruments across diverse scientific fields.

On q-Hermite–Hadamard Type Inequalities via s-Convexity and (α,m)-Convexity

The purpose of the paper is to present new q-parametrized Hermite–Hadamard-like type integral inequalities for functions whose third quantum derivatives in absolute values are s-convex and (α,m)-convex, respectively. Two new q-integral identities are presented for three time q-differentiable functions. These lemmas are used like basic elements in our proofs, along with several important tools like q-power mean inequality, and q-Holder’s inequality. In a special case, a non-trivial example is considered for a specific parameter and this case illustrates the investigated results. We make links between these findings and several previous discoveries from the literature.

Hermite-Hadamard Inequalities Type Using Fractional Integrals for MT-convex Stochastic Process

By applying the standard fractional integral operator of Riemann-Liouville on MT-convex stochastic processes, we can obtain new inequalities of Hermite-Hadamard, providing in the process new estimates on these types of Hermite-Hadamard inequalities for stochastic process whose first derivatives absolute values are MT-convex.

New Perspectives of Symmetry Conferred by q-Hermite-Hadamard Type Integral Inequalities

The main goal of this work is to provide quantum parametrized Hermite-Hadamard like type integral inequalities for functions whose second quantum derivatives in absolute values follow different type of convexities. A new quantum integral identity is derived for twice quantum differentiable functions, which is used as a key element in our demonstrations along with several basic inequalities such as: power mean inequality, and Holder’s inequality. The symmetry of the Hermite-Hadamard type inequalities is stressed by the different types of convexities. Several special cases of the parameter are chosen to illustrate the investigated results. Four examples are presented.

A Note on Fractional Simpson Type Inequalities for Twice Differentiable Functions

ABSTRACT In this paper, an equality is proved for twice differentiable convex functions involving Riemann–Liouville fractional integral. With the help of this equality, there are established several fractional Simpson type inequalities for functions whose second derivatives in absolute value are convex. By using special cases of the main results, previously obtained Simpson type inequalities are found for the Riemann–Liouville fractional integral.

Some New Jensen–Mercer Type Integral Inequalities via Fractional Operators

In this study, we present new variants of the Hermite–Hadamard inequality via non-conformable fractional integrals. These inequalities are proven for convex functions and differentiable functions whose derivatives in absolute value are generally convex. Our main results are established using the classical Jensen–Mercer inequality and its variants for (h,m)-convex modified functions proven in this paper. In addition to showing that our results support previously known results from the literature, we provide examples of their application.

General Lebesgue integral inequalities of Jensen and Ostrowski type and applications

Jensen-Ostrowski-type inequalities for general Lebesgue integral are discussed. Here, we derive information inequalities for Lipschitzian derivatives by using new [Formula: see text]-divergence measure which will be useful in Information Theory. In this way, we establish some particular cases of these information inequalities. We also obtain information inequalities for general Lebesgue integral of differentiable functions whose derivatives in absolute value are [Formula: see text]-convex and its particular instances are established.

THE PARAMETERIZED INTEGRAL INEQUALITIES INVOLVING TWICE-DIFFERENTIABLE GENERALIZED n-POLYNOMIAL CONVEXITY UNDER THE FRAMEWORK OF FRACTAL DOMAINS AND ITS APPLICATIONS

A fractal integral identity with the parameter [Formula: see text] related to twice-differentiable mappings is first proposed in this paper. Based on the identity, the parameterized inequalities over the fractal domains are then derived for the mappings whose second-order derivatives in absolute value at certain powers are generalized [Formula: see text]-polynomial convex, which is the main purpose of this investigation. Moreover, a series of fractal findings of some applications, involving the special mean values, the midpoint formulas, the moments of random variable and the wave equations on Cantor sets, are acquired correspondingly.

On n-fractional polynomial P-functions

In this paper, we introduce and study the concept of n-fractional polynomial P-functions and establish Hermite-Hadamard?s inequalities for this type of functions. In addition, we obtain some new Hermite-Hadamard type inequalities for functions whose first derivative in absolute value is n-fractional polynomial P-functions by using H?lder and power-mean integral inequalities. We also extend our initial results to functions of several variables. Next, we point out some applications of our results to give estimates for the approximation error of the integral the function in the trapezoidal formula and for some inequalities related to special means of real numbers.

Harmonic trigonometrically convexity

In this study, weintroduce and study the concept of harmonic trigonometrically convex functions and their some algebric properties. We prove two Hermite-Hadamard type inequalities for the newly introduced class of functions. We also obtain some refinements of the Hermite-Hadamard inequality for functions whose first derivative in absolute value, raised to a certain power which is greater than one, respectively at least one, is harmonic trigonometrically convex.

The Hermite-Hadamard type inequalities for quasi $ p $-convex functions

<abstract><p>In this paper, the Hermite-Hadamard inequality and its generalization for quasi $ p $-convex functions are provided. Also several new inequalities are established for the functions whose first derivative in absolute value is quasi $ p $-convex, which states some bounds for sides of the Hermite-Hadamard inequalities. In the context of the applications of results, we presented some relations involving special means and some inequalities for special functions including digamma function and Fresnel integral for sinus. In addiditon, an upper bound for error in numerical integration of quasi p-convex functions via composite trapezoid rule is given.</p></abstract>

New parameterized inequalities for twice differentiable functions

The present paper first establishes that an identity involving generalized fractional integrals is proved for twice differentiable functions by using a parameter. By using this equality, we obtain some parameterized inequalities for the functions whose second derivatives in absolute value are convex. Finally, we show that our main results reduce to trapezoid, midpoint Simpson and Bullen-type inequalities which are proved in earlier published papers.

Fractional midpoint-type inequalities for twice-differentiable functions

In this research article, we obtain an identity for twice differentiable functions whose second derivatives in absolute value are convex. By using this identity, we prove several left Hermite-Hadamardtype inequalities for the case of Riemann-Liouville fractional integrals. Furthermore, we provide our results by using special cases of obtained theorems.

A note on fractional Simpson-like type inequalities for functions whose third derivatives are convex

In this paper, equality is established for Riemann-Liouville fractional integral. With the aid of this equality, it is proved some fractional Simpson-like type inequalities for functions whose third derivatives in absolute value are convex. By using special cases of the main results, previously obtained Simpson type inequalities are found for the Riemann-Liouville fractional integral. Furthermore, the mathematical example is presented to verify the newly established inequality.