Results 41 to 50 of about 4,267,250 (176)

Cauchy-Riemann Equations for Free Noncommutative Functions [PDF]

, 2020
In classical complex analysis analyticity of a complex function $f$ is equivalent to differentiability of its real and imaginary parts $u$ and $v$, respectively, together with the Cauchy-Riemann equations for the partial derivatives of $u$ and $v$. We extend this result to the context of free noncommutative functions on tuples of matrices of arbitrary ...
ter Horst, S, Klem, E. M.
openaire   +2 more sources

Functional equations and the Cauchy mean value theorem [PDF]

Aequationes mathematicae, 2016
14 pages, 3 ...
Balogh, Zoltán M., Ibrogimov, Orif O., Mityagin, Boris S.   +2 more
openaire   +3 more sources

Partial difference equations arising from the Cauchy-Riemann equations

Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica, 2006
We consider some functional equations arising from the Cauchy-Riemann equations, and certain related functional equations. First we propose a new functional equation (E.1) below, over a $2$-divisible Abelian group, which is a discrete version of the ...
S. Haruki, S. Nakagiri
doaj  

A Fixed Point Approach to Superstability of Generalized Derivations on Non-Archimedean Banach Algebras

Abstract and Applied Analysis, 2011
We investigate the superstability of generalized derivations in non-Archimedean algebras by using a version of fixed point theorem via Cauchy functional equation.
M. Eshaghi Gordji, M. B. Ghaemi, Badrkhan Alizadeh   +2 more
doaj   +1 more source

The Cauchy-Riemann Differential Equations of Complex Functions [PDF]

Formalized Mathematics, 2009
Summary. In this article we prove Cauchy-Riemann dierential equations of complex functions. These theorems give necessary and sucient condition for dierentiable function.
Hiroshi Yamazaki, Yasunari Shidama, Chanapat Pacharapokin, Yatsuka Nakamura   +3 more
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On a conditional Cauchy functional equation of several variables and a characterization of multivariate stable distributions

International Journal of Mathematics and Mathematical Sciences, 1993
The general solution of a conditional Cauchy functional equation of several variables is obtained and its applications to the characterizations of multivariate stable distributions are studied.
Arjun K. Gupta, Truc T. Nguyen, Wei-Bin Zeng   +2 more
doaj   +1 more source

The Cauchy functional equations in distributions [PDF]

Proceedings of the American Mathematical Society, 1989
The Pompeiu functional equation is defined by Neagu for Schwartz distributions. His method is extended to the four Cauchy functional equations by means of two new operators Q
openaire   +1 more source

A Fixed Point Approach to the Stability of a Functional Equation of the Spiral of Theodorus

Fixed Point Theory and Applications, 2008
Cădariu and Radu applied the fixed point method to the investigation of Cauchy and Jensen functional equations. In this paper, we adopt the idea of Cădariu and Radu to prove the stability of a functional equation of the spiral of Theodorus, f(x+1)=(
John Michael Rassias, Soon-Mo Jung
doaj   +2 more sources

A Generalization of the Cauchy-Schwarz Inequality with Four Free Parameters and Applications [PDF]

, 2008
A generalization of the well-known Cauchy-Schwarz inequality with four free parameters is given for both discrete and continuous cases.
Masjed-Jamei, Mohammad, Dragomir, Sever S   +1 more
core   +4 more sources

Stability of Quadratic Functional Equations via the Fixed Point and Direct Method

Journal of Inequalities and Applications, 2010
Cădariu and Radu applied the fixed point theorem to prove the stability theorem of Cauchy and Jensen functional equations. In this paper, we prove the generalized Hyers-Ulam stability via the fixed point method and investigate new theorems via ...
Juri Lee, Eunyoung Son, Hark-Mahn Kim
doaj   +2 more sources