Integral Inequalities For Convex Functions Research Articles

Tensorial and Hadamard Product Integral Inequalities for Convex Functions of Continuous Fields of Operators in Hilbert Spaces

Let H be a Hilbert space and Ω a locally compact Hausdorff space endowed with a Radon measure μ with ∫_{Ω}1dμ(t)=1. In this paper we show among others that, if f is continuous differentiable convex on the open interval I, (A_{τ})_{τ∈Ω} is a continuous field of positive operators in B(H) such that Sp(A_{τ}) ⊂I for each τ∈Ω and B and operator such that Sp(B)⊂I, then we have ∫_{Ω}(f′(A_{τ})A_{τ})dμ(τ)⊗1-∫_{Ω}f′(A_{τ})dμ(τ)⊗B ≥∫_{Ω}f(A_{τ})dμ(τ)⊗1-1⊗f(B) ≥(∫_{Ω}A_{τ}dμ(τ)⊗1-(1⊗B))(1⊗f′(B)) and the Hadamard product inequality ∫_{Ω}(f′(A_{τ})A_{τ})dμ(τ)∘1-∫_{Ω}f′(A_{τ})dμ(τ)∘B ≥∫_{Ω}f(A_{τ})dμ(τ)∘1-1∘f(B) ≥∫_{Ω}A_{τ}dμ(τ)∘f′(B)-1∘(f′(B)B).

Quantum symmetric integral inequalities for convex functions

In the context of quantum symmetric calculus, this study proposed more refined version of Ostrowski and Hermite–Hadamard type inequalities. The function involved in these inequalities are convex functions. In order to reach the target, left and right quantum symmetric derivative and corresponding integral are used. Furthermore, the Hölder inequality is established in the frame work of left and right quantum symmetric integral. The new results refined the results about integral inequalities that exist in the literature.

Certain Weighted Fractional Integral Inequalities for Convex Functions

In this study, by using the monotonicity properties of functions, several inequalities for convex functions are obtained with the help of a weighted fractional integral operator which provides a function f to be integrated in fractional order with respect to another function. It is also seen that the results obtained were generalizations of the previous results presented.

Several Quantum Hermite–Hadamard-Type Integral Inequalities for Convex Functions

The aim of this study was to present several improved quantum Hermite–Hadamard-type integral inequalities for convex functions using a parameter. Thus, a new quantum identity is proven to be used as the main tool in the proof of our results. Consequently, in some special cases several new quantum estimations for q-midpoints and q-trapezoidal-type inequalities are derived with an example. The results obtained could be applied in the optimization of several economic geology problems.

On the Generalized Inequalities for Co-Ordinated Convex Functions

Abstract The aim of this paper is to establish some generalized integral inequalities for convex functions of 2-variables on the co-ordinat. Then, we will give a generalized identity and with the help of this integral identity, we will investigate some integral inequalities connected with the right hand side of the Hermite-Hadamard type inequalities involving Riemann integrals and Riemann-Liouville fractional integrals.

Hermite-Hadamard-Type Integral Inequalities for Convex Functions and Their Applications

In this paper, we establish new generalizations of the Hermite-Hadamard-type inequalities. These inequalities are formulated in terms of modules of certain powers of proper functions. Generalizations for convex functions are also considered. As applications, some new inequalities for the digamma function in terms of the trigamma function and some inequalities involving special means of real numbers are given. The results also include estimates via arithmetic, geometric and logarithmic means. The examples are derived in order to demonstrate that some of our results in this paper are more exact than the existing ones and some improve several known results available in the literature. The constants in the derived inequalities are calculated; some of these constants are sharp. As a visual example, graphs of some technically important functions are included in the text.

Some New Integral Inequalities for Convex Functions in (p,q)-Calculus

This paper presents Opial and Steffensen inequalities and also discussed q and (p,q)-calculus. Methods of convexity, (p,q)-differentiability and monotonicity of functions were employed in the analyses and new results related to the Opial's-type inequalities were established.

New Fractional Integral Inequalities for Convex Functions Pertaining to Caputo–Fabrizio Operator

In this article, a generalized midpoint-type Hermite–Hadamard inequality and Pachpatte-type inequality via a new fractional integral operator associated with the Caputo–Fabrizio derivative are presented. Furthermore, a new fractional identity for differentiable convex functions of first order is proved. Then, taking this identity into account as an auxiliary result and with the assistance of Hölder, power-mean, Young, and Jensen inequality, some new estimations of the Hermite-Hadamard (H-H) type inequality as refinements are presented. Applications to special means and trapezoidal quadrature formula are presented to verify the accuracy of the results. Finally, a brief conclusion and future scopes are discussed.

Some Generalized Fractional Integral Inequalities for Convex Functions with Applications

In this paper, we establish a generalized fractional integrals identity involving some parameters and differentiable functions. Then, we use the newly established identity and prove different generalized fractional integrals inequalities like midpoint inequalities, trapezoidal inequalities and Simpson’s inequalities for differentiable convex functions. Finally, we give some applications of newly established inequalities in the context of quadrature formulas.

Riemann-Liouville Fractional Versions of Hadamard inequality for Strongly m-Convex Functions

This paper deals with Hadamard inequalities for strongly m-convex functions via Riemann-Liouville fractional integrals. These inequalities provide refinements of well known fractional integral inequalities for convex functions. Further, by applying an identity error estimations are obtained and compared with already known error estimations.

Generalizations of Hermite–Hadamard Type Integral Inequalities for Convex Functions

In the paper, with the help of two known integral identities and by virtue of the classical Hölder integral inequality, the authors establish several new integral inequalities of the Hermite–Hadamard type for convex functions. These newly established inequalities generalize some known results.

New generalized Riemann-Liouville fractional integral inequalities for convex functions

New generalized Riemann-Liouville fractional integral inequalities for convex functions

Generalized proportional fractional integral inequalities for convex functions

<abstract><p>In this paper, we establish some inequalities for convex functions by applying the generalized proportional fractional integral. Some new results by using the linkage between the proportional fractional integral and the Riemann-Liouville fractional integral are obtained. Moreover, we give special cases of our reported results. Obtained results provide generalizations for some of the current results in the literature by applying some special values to the parameters.</p></abstract>

Tempered Fractional Integral Inequalities for Convex Functions

Certain new inequalities for convex functions by utilizing the tempered fractional integral are established in this paper. We also established some new results by employing the connections between the tempered fractional integral with the (R-L) fractional integral. Several special cases of the main result are also presented. The obtained results are more in a general form as it reduced certain existing results of Dahmani (2012) and Liu et al. (2009) by employing some particular values of the parameters.

Modification of certain fractional integral inequalities for convex functions

We consider the modified Hermite–Hadamard inequality and related results on integral inequalities, in the context of fractional calculus using the Riemann–Liouville fractional integrals. Our results generalize and modify some existing results. Finally, some applications to special means of real numbers are given. Moreover, some error estimates for the midpoint formula are pointed out.

Certain Fractional Proportional Integral Inequalities via Convex Functions

The goal of this article is to establish some fractional proportional integral inequalities for convex functions by employing proportional fractional integral operators. In addition, we establish some classical integral inequalities as the special cases of our main findings.

New Hermite–Hadamard type integral inequalities for convex functions and their applications

In this paper, we establish (presumably new type) integral inequalities for convex functions via the Hermite–Hadamard’s inequalities. As applications, we apply these new inequalities to construct inequalities involving special means of real numbers, some error estimates for the formula midpoint are given. Finally, new inequalities for some special and q -special functions are also pointed out.

Some Riemann–Liouville fractional integral inequalities for convex functions

We are pleased to investigate some Riemann–Liouville fractional integral inequalities in a very simple and novel way. By using convexity of a function f and a simple inequality over the domain of f we establish some interesting results.

Simpson type quantum integral inequalities for convex functions

Simpson type quantum integral inequalities for convex functions

Generalized integral inequalities for convex functions

Generalized integral inequalities for convex functions