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.

scholarly journals Simpson’s Second-Type Inequalities for Co-Ordinated Convex Functions and Applications for Cubature Formulas

2022 ◽  
Vol 6 (1) ◽  
pp. 33
Author(s):  
Sabah Iftikhar ◽  
Samet Erden ◽  
Muhammad Aamir Ali ◽  
Jamel Baili ◽  
Hijaz Ahmad
Keyword(s):  
Convex Functions ◽  
Cubature Formula ◽  
Applied Mathematics ◽  
Second Order ◽  
Absolute Value ◽  
Partial Derivatives ◽  
Cubature Formulas ◽  
Inequality Theory ◽  
Type Integral ◽  
Derivatives Of

Inequality theory has attracted considerable attention from scientists because it can be used in many fields. In particular, Hermite–Hadamard and Simpson inequalities based on convex functions have become a cornerstone in pure and applied mathematics. We deal with Simpson’s second-type inequalities based on coordinated convex functions in this work. In this paper, we first introduce Simpson’s second-type integral inequalities for two-variable functions whose second-order partial derivatives in modulus are convex on the coordinates. In addition, similar results are acquired by considering that powers of the absolute value of second-order partial derivatives of these two-variable functions are convex on the coordinates. Finally, some applications for Simpson’s 3/8 cubature formula are given.

Analogical Modelling and Numerical Simulation of the Adsorption Process for Poly-Phenothiazine Formaldehyde on Graphite Electrodes

2010 ◽  
Vol 7 (1) ◽  
Author(s):  
Mihaela-Ligia M. Unguresan ◽  
Delia Maria Gligor ◽  
Francisc Dulf ◽  
Tiberiu Colosi
Keyword(s):  
Numerical Simulation ◽  
Taylor Series ◽  
Adsorption Process ◽  
Phenothiazine Derivative ◽  
Graphite Electrodes ◽  
Partial Derivatives ◽  
Independent Variables ◽  
Regulation Scheme ◽  
Derivatives Of ◽  
Two Independent Variables

The paper presents the dispersion of the concentration y(t, s) on the length (s) with respect to time (t), corresponding to the adsorption process of a phenothiazine derivative on graphite electrodes. The numerical simulation by equations with partial derivatives of the second order with two independent variables (t and s) (PDE II.2), based on (Mpdx) which associates with Taylor series was performed. Also, the adsorption process defined by PDE II.2 was included in a regulation scheme of concentration y(t, s) with multiple freedom levels. It insures good performances and a remarkable flexibility for extending the method in similar categories of applications.

An Ostrowski type inequality for derivatives of q-th power of s-convex functions via fractional integrals

2014 ◽  
Vol 0 (0) ◽  
Author(s):  
Muhamet Emin Özdemir ◽  
Çetin Yildiz
Keyword(s):  
Convex Functions ◽  
Type Inequality ◽  
Fractional Integrals ◽  
Ostrowski Type Inequality ◽  
Derivatives Of ◽  
New Inequalities

AbstractIn this paper, we establish several new inequalities for

New generalized 2D Ostrowski type inequalities on time scales with k2 points using a parameter

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3155-3169 ◽  
Author(s):  
Seth Kermausuor ◽  
Eze Nwaeze
Keyword(s):  
Numerical Analysis ◽  
Time Scales ◽  
Type Inequality ◽  
Dimensional Case ◽  
Multiple Points ◽  
Quantum Calculus ◽  
Independent Variables ◽  
Ostrowski Type Inequality ◽  
Two Independent Variables

Recently, a new Ostrowski type inequality on time scales for k points was proved in [G. Xu, Z. B. Fang: A Generalization of Ostrowski type inequality on time scales with k points. Journal of Mathematical Inequalities (2017), 11(1):41-48]. In this article, we extend this result to the 2-dimensional case. Besides extension, our results also generalize the three main results of Meng and Feng in the paper [Generalized Ostrowski type inequalities for multiple points on time scales involving functions of two independent variables. Journal of Inequalities and Applications (2012), 2012:74]. In addition, we apply some of our theorems to the continuous, discrete, and quantum calculus to obtain more interesting results in this direction. We hope that results obtained in this paper would find their place in approximation and numerical analysis.

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