scholarly journals On Hermite-Hadamard Type Inequalities for Coordinated Convex Functions via (p,q)-Calculus

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 698
Author(s):  
Fongchan Wannalookkhee ◽  
Kamsing Nonlaopon ◽  
Jessada Tariboon ◽  
Sotiris K. Ntouyas
Keyword(s):  
Convex Functions ◽  
Continuous Functions ◽  
Functions Of Two Variables

In this paper, we define (p,q)-integrals for continuous functions of two variables. Then, we prove the Hermite-Hadamard type inequalities for coordinated convex functions by using (p,q)-integrals. Many results obtained in this paper provide significant extensions of other related results given in the literature. Finally, we give some examples of our results.

Smooth approximations by continuous choice-functions

2021 ◽  
Author(s):  
Mihai Prunescu
Keyword(s):  
Error Bound ◽  
Common Sense ◽  
Choice Function ◽  
Continuous Functions ◽  
Ordered Sets ◽  
Choice Functions ◽  
Continuous Choice ◽  
Functions Of Two Variables ◽  
Smooth Approximations

Abstract We explore the existence of rational-valued approximation processes by continuous functions of two variables, such that the output continuously depends of the imposed error-bound. To this sake we prove that the theory of densely ordered sets with generic predicates is ℵ0- categorical. A model of the theory and a particular continuous choice-function are constructed. This function transfers to all other models by the respective isomorphisms. If some common-sense conditions are fulfilled, the processes are computable. As a byproduct, other functions with surprising properties can be constructed.

scholarly journals Some (p,q)-Estimates of Hermite-Hadamard-Type Inequalities for Coordinated Convex and Quasi- Convex Functions

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 683 ◽  
Author(s):  
Humaira Kalsoom ◽  
Muhammad Amer ◽  
Moin-ud-Din Junjua ◽  
Sabir Hussain ◽  
Gullnaz Shahzadi
Keyword(s):  
Convex Functions ◽  
Integral Type ◽  
Partial Derivatives ◽  
Functions Of Two Variables ◽  
Right Hand ◽  
The Absolute ◽  
The Right ◽  
Quasi Convexity

In this paper, we present the preliminaries of ( p , q ) -calculus for functions of two variables. Furthermore, we prove some new Hermite-Hadamard integral-type inequalities for convex functions on coordinates over [ a , b ] × [ c , d ] by using the ( p , q ) -calculus of the functions of two variables. Furthermore, we establish an identity for the right-hand side of the Hermite-Hadamard-type inequalities on coordinates that is proven by using the ( p , q ) -calculus of the functions of two variables. Finally, we use the new identity to prove some trapezoidal-type inequalities with the assumptions of convexity and quasi-convexity on coordinates of the absolute values of the partial derivatives defined in the ( p , q ) -calculus of the functions of two variables.

scholarly journals Approximation by Certain Linear Positive Operators of Two Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Afşin Kürşat Gazanfer ◽  
İbrahim Büyükyazıcı
Keyword(s):  
Convergence Rate ◽  
Modulus Of Continuity ◽  
Weighted Approximation ◽  
Continuous Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Compact Set ◽  
Approximation Properties ◽  
Linear Positive Operators ◽  
Functions Of Two Variables

We introduce positive linear operators which are combined with the Chlodowsky and Szász type operators and study some approximation properties of these operators in the space of continuous functions of two variables on a compact set. The convergence rate of these operators are obtained by means of the modulus of continuity. And we also obtain weighted approximation properties for these positive linear operators in a weighted space of functions of two variables and find the convergence rate for these operators by using the weighted modulus of continuity.

scholarly journals Post quantum Ostrowski-type inequalities for coordinated convex functions

2021 ◽  
Author(s):  
Fongchan Wannalookkhee ◽  
Kamsing Nonlaopon ◽  
S.K. Ntouyas ◽  
Huseyin Budak
Keyword(s):  
Convex Functions ◽  
Continuous Functions

In this article, we give a new notion of (p,q)-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.

scholarly journals New Hermite-Hadamard type inequalities for m and (α, m)-convex functions on the coordinates via generalized fractional integrals

2021 ◽  
Vol 40 (6) ◽  
pp. 1449-1472
Author(s):  
Seth Kermausuor
Keyword(s):  
Convex Functions ◽  
Type Inequality ◽  
Second Order ◽  
Fractional Integrals ◽  
Absolute Value ◽  
Partial Derivatives ◽  
Independent Variables ◽  
Functions Of Two Variables ◽  
Derivatives Of ◽  
Two Independent Variables

In this paper, we obtained a new Hermite-Hadamard type inequality for functions of two independent variables that are m-convex on the coordinates via some generalized Katugampola type fractional integrals. We also established a new identity involving the second order mixed partial derivatives of functions of two independent variables via the generalized Katugampola fractional integrals. Using the identity, we established some new Hermite-Hadamard type inequalities for functions whose second order mixed partial derivatives in absolute value at some powers are (α, m)-convex on the coordinates. Our results are extensions of some earlier results in the literature for functions of two variables.

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