scholarly journals A NOTE ON TWO DIMENSIONAL INTEGRAL INEQUALITY

1990 ◽  
Vol 21 (3) ◽  
pp. 211-213
Author(s):  
B. G. PACHPATTE
Keyword(s):  
Integral Inequality ◽  
Present Note ◽  
Two Dimensional ◽  
Partial Derivatives ◽  
Independent Variables ◽  
Dimensional Integral ◽  
Two Independent Variables

In the present note we establish a new integral inequality involving a function of two independent variables and its partial derivatives.

scholarly journals On the Generalized Weighted Integral Inequality for Double Integrals

2015 ◽  
Vol 61 (1) ◽  
pp. 169-179 ◽  
Author(s):  
Mehmet Zeki Sarikaya
Keyword(s):  
Integral Inequality ◽  
Independent Variables ◽  
Elementary Analysis ◽  
Weighted Integral ◽  
Function Of Two Variables ◽  
Two Independent Variables ◽  
Double Integrals

Abstract In this paper, we obtain weighted Montgomery’s identities for function of two variables and apply them to give new generalization weighted integral inequality for double integrals involving functions of two independent variables by using fairly elementary analysis.

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 On a new Ostrowski type inequality in two independent variables

2001 ◽  
Vol 32 (1) ◽  
pp. 45-49
Author(s):  
B. G. Pachpatte
Keyword(s):  
Integral Inequality ◽  
Type Inequality ◽  
Discrete Analogue ◽  
Independent Variables ◽  
Ostrowski Type Inequality ◽  
Two Independent Variables

In this note a new integral inequality of Ostrowski type in two independent variables is established. The discrete analogue of the main result is also given.

scholarly journals On the Ostrowski type integral inequality for double integrals

2012 ◽  
Vol 45 (3) ◽  
Author(s):  
Mehmet Zeki Sarikaya
Keyword(s):  
Integral Inequality ◽  
Independent Variables ◽  
Elementary Analysis ◽  
Type Integral ◽  
Two Independent Variables ◽  
Double Integrals

AbstractIn this note, we establish a new inequality of Ostrowski-type for double integrals involving functions of two independent variables by using fairly elementary analysis.

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.

scholarly journals Proof of the Conditions for a Turning Value of f (x, y) without the use of Taylor's Theorem

1927 ◽  
Vol 1 (1) ◽  
pp. 68-70
Author(s):  
John McWhan
Keyword(s):  
Standard Method ◽  
Partial Derivatives ◽  
Independent Variables ◽  
Minimum Value ◽  
Elementary Knowledge ◽  
Two Independent Variables ◽  
Critical Consideration

The standard method of establishing rigidly the tests for a maximum or minimum value of a function of two independent variables, depending as it does on the use of Taylor's Theorem and on a very critical consideration of the Remainder in that theorem, presents difficulties so considerable that it is not surprising that most text-books on the Calculus frankly decline to enter on the discussion, and assume the necessity and sufficiency of the well known Lagrange's Condition. It is the object of this paper to show that a satisfactory proof of the tests may be given, from the purely geometrical standpoint, without recourse to Taylor's Theorem. The method requires only an elementary knowledge of the process of changing the independent variables in partial derivatives, and may therefore be introduced comparatively early in the Calculus course.

scholarly journals Some properties of approximants for branched continued fractions of the special form with positive and alternating-sign partial numerators

2018 ◽  
Vol 10 (1) ◽  
pp. 3-13 ◽  
Author(s):  
T.M. Antonova ◽  
M.V. Dmytryshyn ◽  
S.M. Vozna
Keyword(s):  
Continued Fractions ◽  
Special Form ◽  
Sufficient Conditions ◽  
Two Dimensional ◽  
Rational Approximants ◽  
Independent Variables ◽  
Function Of Two Variables ◽  
Necessary And Sufficient ◽  
Double Power Series ◽  
Two Independent Variables

The paper deals with research of convergence for one of the generalizations of continued fractions -- branched continued fractions of the special form with two branches. Such branched continued fractions, similarly as the two-dimensional continued fractions and the branched continued fractions with two independent variables are connected with the problem of  the correspondence between a formal double power series and a sequence of the rational approximants of a function of two variables. Unlike continued fractions, approximants of which are constructed unambiguously, there are many ways to construct approximants of branched continued fractions of the general and the special form. The paper examines the ordinary approximants and one of the structures of figured approximants of the studied branched continued fractions, which is connected with the problem of correspondence. We consider some properties of approximants of such fractions, whose partial numerators are positive and alternating-sign  and partial denominators are equal to one. Some necessary and sufficient conditions for figured convergence are established. It is proved that under these conditions from the convergence of the sequence of figured approximants it follows the convergence of the sequence of ordinary approximants  to the same limit.

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