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Orthogonal polynomials and expansions for a family of weight functions in two variables
Orthogonal polynomials orthogonal expansions Jacobi polynomials
2011/2/25
Orthogonal polynomials for a family of weight functions on [1; 1]2,W ; ; (x; y) = jx + yj2 +1jx yj2 +1(1 x2) (1 y2) ; are studied and shown to be related to ...
Limits of quotients of real analytic functions in two variables
quotients real analytic functions variables
2010/11/12
Necessary and sufficient conditions for the existence of limits of the form {equation*} \lim_{(x,y)\rightarrow (a,b)}\frac{f(x,y)}{g(x,y)} {equation*} are given, under the hipothesis that $f$ and $g$...
Volterra Integral and Integrodifferential Equations in Two Variables
Volterra integral and integrodifferential equations Banach fixed point theorem Bielecki type norm integral inequalities existence and uniqueness estimates on the solutions approximate solutions
2010/4/16
The aim of this paper is to study the existence, uniqueness and other properties of solutions of certain Volterra integral and integrodifferential equations in two variables. The tools employed in the...
We show that certain inequalities for the means A, G, L, I proved by H.-J. Seiffert [12] as well as by H. Alzer and S.-L. Qiu [3] are consequences of some results of the author [5], [7], [9].
A study of a two variables Gegenbauer polynomials
Gegenbauer polynomial partial differential equation
2010/9/10
The present paper deals with a study udy of a two variable polynomial y) (x, C k , n
νanalogous to the Gegenbauer polynomial (x) Cn ν . The paper contains differential
recurrence relations, a partia...
Extending Means of Two Variables to Several Variables
Means Logarithmic mean Divided differences Series expansions Symmetric polynomials
2008/7/1
We present a method, based on series expansions and symmetric polynomials, by which a mean of two variables can be extended to several variables. We apply it mainly to the logarithmic mean.
Note on Certain Inequalities for Means in Two Variables
Arithmetic mean Geometric mean Identric mean
2008/6/27
Note on Certain Inequalities for Means in Two Variables.
On an Inequality of V. Csiszár and T.F. Móri for Concave Functions of Two Variables
Diaz-Metcalf inequality Hö lder's inequality Hadamard's inequality Petrović 's inequality Giaccardi's inequality
2008/6/27
V. Csiszár and T.F. Móri gave an extension of Diaz-Metcalf's inequality for concave functions. In this paper, we show its restatement. As its applications we first give a reverse inequality of Hö...
Some Retarded Nonlinear Integral Inequalities in Two Variables and Applications
Integral inequality Nonlinear Two variables Retarded
2010/1/22
In this paper, some retarded nonlinear integral inequalities in two variables with more than one distinct nonlinear term are established. Our results are also applied to show the boundedness of the so...