Co-ordinated Convex Functions Research Articles

New Results on Simpson-Type Inequalities for Co-ordinated Convex Function by Generalized Conformable Integrals

In this paper, firstly, we prove an identity involving generalized conformable integrals. By using this obtained identity, we establish several Simpson-type inequalities for differentiable co-ordinated convex function by means of generalized conformable fractional integrals. More precisely, some Simpson-type inequalities are obtained using the well-known Hölder and Power mean inequalities. Furthermore, we also consider some special cases which can be deduced from the main results.

New version of midpoint-type inequalities for co-ordinated convex functions via generalized conformable integrals

In the current research, some midpoint-type inequalities are generalized for co-ordinated convex functions with the help of generalized conformable fractional integrals. Moreover, some findings of this paper include results based on Riemann–Liouville fractional integrals and Riemann integrals.

Symmetric Quantum Inequalities on Finite Rectangular Plane

Finding the range of coordinated convex functions is yet another application for the symmetric Hermite–Hadamard inequality. For any two-dimensional interval [a0,a1]×[c0,c1]⊆ℜ2, we introduce the notion of partial qθ-, qϕ-, and qθqϕ-symmetric derivatives and a qθqϕ-symmetric integral. Moreover, we will construct the qθqϕ-symmetric Hölder’s inequality, the symmetric quantum Hermite–Hadamard inequality for the function of two variables in a rectangular plane, and address some of its related applications.

On Hermite-Hadamard type inequalities for co-ordinated convex function via conformable fractional integrals

<abstract><p>In this study, some new Hermite-Hadamard type inequalities for co-ordinated convex functions were obtained with the help of conformable fractional integrals. We have presented some remarks to give the relation between our results and earlier obtained results. Moreover, an identity for partial differentiable functions has been established. By using this equality and concept of co-ordinated convexity, we have proven a trapezoid type inequality for conformable fractional integrals.</p></abstract>

Q-Hermite-Hadamard Integral Inequality for the Coordinated Convex Functions

The calculus without the notion of limits is quantum calculus. Its study dates back to L. Euler in the middle of the eighteenth century whereas the systematic initiation on it was done by F.H. Jackson in the beginning of the twentieth century. The rapid growth on q-calculus is due to its applications in various branches of mathematical and physical sciences. Of them, one of the most basic and important functions in the theory of geometric function is convexity having its wider applications in pure and applied mathematics. As it still lacks the intensive study on quantum estimates on the various types of integral inequalities, we focus our study on quantum estimates of Hermite-Hadamard type integral inequality especially on coordinated convex functions. In this paper, we have extended Hermite-Hadamard type integral inequality for coordinated convex function in terms of quantum framework.

On some generalized Simpson type inequalities for (α,m)-coordinated convex functions in context of q 1 q 2-calculus

Abstract In the current investigation, we offer the generalized version of q 1 ⁢ q 2 {q_{1}q_{2}} -Simpson’s type inequalities via ( α , m ) {(\alpha,m)} -coordinated convex functions. To validate their generalized behavior, we demonstrate the link between our outcomes and the already derived ones. Moreover, we provide some application to special means of positive real numbers to support our findings. The principal outcomes raised in this investigation are extensions and generalizations of the comparable results in the history on Simpson’s inequalities for coordinated convex functions.

Raina’s Function-Based Formulations of Right-Sided Simpson’s and Newton’s Inequalities for Generalized Coordinated Convex Functions

The main focus of this article is to derive some new counterparts to Simpson’s and Newton’s type inequalities involve a class of generalized coordinated convex mappings. This class contains several new and known classes of convexity as special cases. For further demonstration, we deploy the concept of right quantum derivatives to develop two new identities involving Raina’s function. Moreover, by implementing these auxiliary results together with generalized convexity, we acquire a Holder-type inequality. We also acquire some applications of our main findings by making use of suitable substitutions in Raina’s function.

A Comprehensive Review of the Hermite–Hadamard Inequality Pertaining to Quantum Calculus

A review of results on Hermite–Hadamard (H-H) type inequalities in quantum calculus, associated with a variety of classes of convexities, is presented. In the various classes of convexities this includes classical convex functions, quasi-convex functions, p-convex functions, (p,s)-convex functions, modified (p,s)-convex functions, (p,h)-convex functions, tgs-convex functions, η-quasi-convex functions, ϕ-convex functions, (α,m)-convex functions, ϕ-quasi-convex functions, and coordinated convex functions. Quantum H-H type inequalities via preinvex functions and Green functions are also presented. Finally, H-H type inequalities for (p,q)-calculus, h-calculus, and (q−h)-calculus are also included.

Hermite–Hadamard-Type Inequalities for Coordinated Convex Functions Using Fuzzy Integrals

In this paper, some estimates of third and fourth inequalities in Hermite–Hadamard-type inequalities for coordinated convex functions are proved using the non-additivity of the integrals and Fubini’s theorem for fuzzy integrals. That is, the results are obtained in the fuzzy context and using the Lebesgue measure. Several examples are provided on how to evaluate these estimates in order to illustrate the obtained results.

New Estimation of Error in the Hadamard Inequality Pertaining to Coordinated Convex Functions in Quantum Calculus

Convex bodies are symmetric in nature. Between the two variables of symmetry and convexity, a correlation connection is also perceptible. Due to the interchangeable analogous properties, the application on either of them has been practicable in these modern years. The current analysis sheds insight on a general new identity involving a number of parameters for a twice partial quantum differentiable function. We find several unique quantum integral inequalities by using the new identity and a twice partial quantum differentiable function whose absolute value is coordinated convex. In addition, we present several novel and interesting error estimation-like results related to the well-known quantum Hermite–Hadamard inequality. Some examples are provided at the end to support and demonstrate the effectiveness of the new outcomes.

On some new quantum trapezoid-type inequalities for q-differentiable coordinated convex functions

In this paper, we establish several new inequalities for q-differentiable coordinated convex functions that are related to the right side of Hermite–Hadamard inequalities for coordinated convex functions. We also show that the inequalities proved in this paper generalize the results given in earlier works. Moreover, we give some examples in order to demonstrate our main results.

On inequalities of Simpson type for co-ordinated convex functions via generalized fractional integrals

In this study, we prove equality for twice partially differentiable mappings involving the double generalized fractional integral. Using the established identity, we offer some Simpson?s type inequalities for differentiable co-ordinated convex functions in a rectangle from the plane R2.

Generalized fractional midpoint type inequalities for co-ordinated convex functions

In this research paper, we investigate generalized fractional integrals to obtain midpoint type inequalities for the co-ordinated convex functions. First of all, we establish an identity for twice partially differentiable mappings. By utilizing this equality, some midpoint type inequalities via generalized fractional integrals are proved. We also show that the main results reduce some midpoint inequalities given in earlier works for Riemann integrals and Riemann-Liouville fractional integrals. Finally, some new inequalities for k-Riemann-Liouville fractional integrals are presented as special cases of our results.

On the generalized Ostrowski type inequalities for co-ordinated convex functions

The purpose of this article is to establish some generalized Ostrowski type inequalities and integral inequalities in the coordinate plane for convex functions of 2 variables. For this, we will specify a generalized identity, and with the help of this integral identity, we will examine the Ostrowski, trapezoid, and midpoint type integral inequalities, including Riemann integral and Riemann-Liouville fractional integral. In this way, we aim to contribute to the generalization of integral inequalities, an important topic in mathematical analysis.

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.

Post quantum Ostrowski‐type inequalities for coordinated convex functions

In this article, we give a new notion of derivatives for continuous functions on coordinates. We also derive post quantum Ostrowski‐type inequalities for coordinated convex functions. Our significant results are considered as the generalizations of other results that appeared in the literature.

On Fractional Newton Inequalities via Coordinated Convex Functions

In this paper, firstly, we present an integral identity for functions of two variables via Riemann–Liouville fractional integrals. Then, a Newton-type inequality via partially differentiable coordinated convex mappings is derived by taking the absolute value of the obtained identity. Moreover, several inequalities are obtained with the aid of the Hölder and power mean inequality. In addition, we investigate some Newton-type inequalities utilizing mappings of two variables with bounded variation. Finally, we gave some mathematical examples and their graphical behavior to validate the obtained inequalities.

On fractional Simpson type integral inequalities for co-ordinated convex functions

In this study, we prove equality for twice partially differentiable mappings involving the double generalized fractional integral. Using the established identity, we offer some Simpson’s type inequalities for partially differentiable co-ordinated convex functions in a rectangle from the plane mathbb{R} ^{2}.

Some New Quantum Hermite–Hadamard Inequalities for Co-Ordinated Convex Functions

In this paper, we establish some new versions of Hermite–Hadamard type inequalities for co-ordinated convex functions via q1,q2-integrals. Since the inequalities are newly proved, we therefore consider some examples of co-ordinated convex functions and show their validity for particular choices of q1,q2∈(0,1). We hope that the readers show their interest in these results.

Some new q-Hermite-Hadamard type inequalities for the product of convex functions

In this paper, we first obtain some q-Hermite-Hadamard type inequalities for the product of two convex functions. Then by using the product of two co-ordinated convex functions, we establish new q-Hermite-Hadamard type inequalities. The results in this work generalize several results obtained in earlier studies.