Co-ordinated Convex Functions Research Articles

On the Hermite\u2013Hadamard inequalities for interval-valued coordinated convex functions

In this work, we introduce the notion of interval-valued coordinated convexity and demonstrate Hermite–Hadamard type inequalities for interval-valued convex functions on the co-ordinates in a rectangle from the plane. Moreover, we prove Hermite–Hadamard inequalities for the product of interval-valued convex functions on coordinates. Our results generalize several other well-known inequalities given in the existing literature on this subject.

Some New Newton’s Type Integral Inequalities for Co-Ordinated Convex Functions in Quantum Calculus

Some recent results have been found treating the famous Simpson’s rule in connection with the convexity property of functions and those called generalized convex. The purpose of this article is to address Newton-type integral inequalities by associating with them certain criteria of quantum calculus and the convexity of the functions of various variables. In this article, by using the concept of recently defined q1q2 -derivatives and integrals, some of Newton’s type inequalities for co-ordinated convex functions are revealed. We also employ the limits of q1,q2→1− in new results, and attain some new inequalities of Newton’s type for co-ordinated convex functions through ordinary integral. Finally, we provide a thorough application of the newly obtained key outcomes, these new consequences can be useful in the integral approximation study for symmetrical functions, or with some kind of symmetry.

Some New Quantum Hermite–Hadamard-Like Inequalities for Coordinated Convex Functions

In this paper, we give some new definitions for quantum integrals of two-variable functions. We establish quantum Hermite–Hadamard-type inequalities for coordinated convex functions via newly defined quantum integrals.

Hermite‐Hadamard‐type inequalities for interval‐valued coordinated convex functions involving generalized fractional integrals

In this paper, we define interval‐valued left‐sided and right‐sided generalized fractional double integrals. We establish inequalities of Hermite‐Hadamard like for coordinated interval‐valued convex functions by applying our newly defined integrals.

Refinement of fejér inequality for convex and co-ordinated convex functions

Abstract In this paper, we shall establish the co-ordinated convex function. It can connect to the right-hand side of Fejér inequality in two variables and thus a new refinement can be found. In addition, some applications to estimates for Euler’s Beta function are also given in the end.

Generalized Hermite-Hadamard type inequalities for products of co-ordinated convex functions

In this paper, we think products of two co-ordinated convex functions for the Hermite-Hadamard type inequalities. Using these functions we obtained Hermite-Hadamard type inequalities which are generalizations of some results given in earlier works.

SCHUR-CONVEXITY OF INTEGRAL ARITHMETIC MEANS OF CO-ORDINATED CONVEX FUNCTIONS IN `R^3`

In this paper, we investigate Schur-convexity of some functions which are obtained from the co-ordinated convex functions on a rectangular box in `R^3`.

New refinements of the Hadamard inequality on coordinated convex function

In this paper, new refinements of the Hadamard inequality on coordinated convex function are established. Besides, a simple proof of the Hadamard type for linear functions is also found. Moreover, some examples of the new refinement inequalities are given to check their validity.

On Extended General Mittag–Leffler Functions and Certain Inequalities

In this paper, we introduce and investigate generalized fractional integral operators containing the new generalized Mittag–Leffler function of two variables. We establish several new refinements of Hermite–Hadamard-like inequalities via co-ordinated convex functions.

Simpson’s Type Inequalities for Co-Ordinated Convex Functions on Quantum Calculus

In the present paper, we aim to prove a new lemma and quantum Simpson’s type inequalities for functions of two variables having convexity on co-ordinates over [ α , β ] × [ ψ , ϕ ] . Moreover, our deduction introduce new direction as well as validate the previous results.

On Hermite-Hadamard type inequalities of coordinated (p1,h1)-(p2,h2)-convex functions via Katugampola fractional integrals

The present article establishes some results on Hermite-Hadamard type inequalities of coordinated (p1,h1)-(p2,h2)-convex functions by using Katugampola fractional integrals. The results are in generalized form and deduced for various special cases like coordinated pq-convex functions, coordinated (p,s)-convex functions, coordinated s-convex functions and classical case of coordinated convex functions.

On the Refined Hermite-Hadamard Inequalities

In this paper, we give some new refinements of Hermite-Hadamard inequality for co-ordinated convex function. These refinements provide us better estimation as compare to the earlier established refinements of Hadamard’s inequality.

On the Hermite-Hadamard s and Ostrowski s inequalities for the co-ordinated convex functions

On the Hermite-Hadamard s and Ostrowski s inequalities for the co-ordinated convex functions

On the Hermite-Hadamard-Fejer-type inequalities for co-ordinated convex functions via fractional integrals

In this paper, using Riemann-Liouville integral operators, we establish new fractional in- tegral inequalities of Hermite-Hadamard-Fejer type for co-ordinated convex functions on a rectangle of R^2. The results presented here would provide extensions of those given in earlier works.

On the refinements of Hadamard-type inequalities and their applications for cubature formulas

In this paper, we shall establish some Hadamard-type inequalities for differentiable coordinated convex functions in a rectangle from the plane in two variables. Through these inequalities, more precise estimates could be obtained. Some examples and applications to cubature formulas are also provided.

On the Hadamard’s type inequalities for co-ordinated convex functions via fractional integrals

In this paper, we establish two identities for functions of two variables and apply them to give new Hermite–Hadamard type fractional integral inequalities for double fractional integrals involving functions whose derivatives are bounded or co-ordinates convex function on Δ≔[a,b]×[c,d] in R2 with a<b,c<d.

Generalization of Some Inequalities for Differentiable Co-ordinated Convex Functions With Applications

Abstract In this paper, a new weighted identity for functions defined on a rectangle from the plane is established. By using the obtained identity and analysis, some new weighted integral inequalities for the classes of co-ordinated convex, co-ordinated wright-convex and co-ordinated quasi-convex functions on the rectangle from the plane are established which provide weighted generalization of some recent results proved for co-ordinated convex functions. Some applications of our results to random variables and 2D weighted quadrature formula are given as well.

English

English

Some New Ostrowski Type Inequalities for Co-Ordinated Convex Functions

In this paper, we obtain new identity for function of two variables and apply them to give new Ostrowski type integral inequality for double integrals involving functions whose derivatives are co-ordinates convex function on ( ) ( ) :, , ab c d ∆= × in 2 R with , a b c d << .

A Generalized Hermite-Hadamard Inequality for Coordinated Convex Function and Some Associated Mappings

We have discussed the generalization of Hermite-Hadamard inequality introduced by Lupaş for convex functions on coordinates defined in a rectangle from the plane. Also we define that mappings are related to it and their properties are discussed.