scholarly journals On a quaternionic Picard theorem

2020 ◽  
Vol 7 (9) ◽  
pp. 106-117 ◽  
Author(s):  
Cinzia Bisi ◽  
Jörg Winkelmann
Keyword(s):  
Picard Theorem

The Topological Nature of Two Noguchi Theorems on Sequences of Holomorphic Mappings Between Complex Spaces

1995 ◽  
Vol 47 (6) ◽  
pp. 1240-1252
Author(s):  
James E. Joseph ◽  
Myung H. Kwack
Keyword(s):  
Function Theory ◽  
Riemann Sphere ◽  
Complex Function ◽  
Holomorphic Extension ◽  
Holomorphic Mappings ◽  
Classical Theorem ◽  
Complex Function Theory ◽  
Topological Methods ◽  
Complex Spaces ◽  
Picard Theorem

AbstractLet C,D,D* be, respectively, the complex plane, {z ∈ C : |z| < 1}, and D — {0}. If P1(C) is the Riemann sphere, the Big Picard theorem states that if ƒ:D* → P1(C) is holomorphic and P1(C) → ƒ(D*) n a s more than two elements, then ƒ has a holomorphic extension . Under certain assumptions on M, A and X ⊂ Y, combined efforts of Kiernan, Kobayashi and Kwack extended the theorem to all holomorphic ƒ: M → A → X. Relying on these results, measure theoretic theorems of Lelong and Wirtinger, and other properties of complex spaces, Noguchi proved in this context that if ƒ: M → A → X and ƒn: M → A → X are holomorphic for each n and ƒn → ƒ, then . In this paper we show that all of these theorems may be significantly generalized and improved by purely topological methods. We also apply our results to present a topological generalization of a classical theorem of Vitali from one variable complex function theory.

scholarly journals Satake compactification and the great Picard theorem

1971 ◽  
Vol 23 (2) ◽  
pp. 340-350 ◽  
Author(s):  
Shoshichi KOBAYASHI ◽  
Takushiro OCHIAI
Keyword(s):  
Picard Theorem

scholarly journals A Picard Theorem for iterative differential equations

2009 ◽  
Vol 42 (2) ◽  
Author(s):  
Wen-rong Li ◽  
Sui Sun Cheng
Keyword(s):  
Differential Equations ◽  
Uniqueness Theorem ◽  
Existence And Uniqueness ◽  
Existence And Uniqueness Theorem ◽  
Picard Theorem ◽  
Iterative Differential Equations

AbstractA Picard type existence and uniqueness theorem is established for iterative differential equations of the form

On Bridges' Proof of the Great Picard Theorem

1982 ◽  
Vol 89 (4) ◽  
pp. 239-239
Author(s):  
Andreana S. Madguerova
Keyword(s):  
Picard Theorem

An improved version of the big Picard theorem for polyanalytic functions

1977 ◽  
Vol 28 (4) ◽  
pp. 337-342 ◽  
Author(s):  
M. B. Balk ◽  
A. A. Gol'dberg
Keyword(s):  
Picard Theorem ◽  
Polyanalytic Functions

scholarly journals A novel difference schemes for analyzing the fractional Navier-Stokes equations

2017 ◽  
Vol 25 (1) ◽  
pp. 195-206
Author(s):  
Khosro Sayevand ◽  
Dumitru Baleanu ◽  
Fatemeh Sahsavand
Keyword(s):  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Discrete Analogue ◽  
Stability And Convergence ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Suggested Approach ◽  
Stokes Problems ◽  
Picard Theorem ◽  
Dimensional Domain

Abstract In this report, a novel difference scheme is used to analyzing the Navier - Stokes problems of fractional order. Existence and uniqueness of the suggested approach with a Lipschitz condition and Picard theorem are proved. Furthermore, we find a discrete analogue of the derivative and then stability and convergence of our strategy in multi dimensional domain are proved.

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