scholarly journals On the fourth and fifth coefficients in the Carathéodory class

Filomat ◽  
2020 ◽  
Vol 34 (6) ◽  
pp. 2061-2072
Author(s):  
Nak Cho ◽  
Bogumiła Kowalczyk ◽  
Adam Lecko ◽  
Barbara Śmiarowska
Keyword(s):  
Carathéodory Class

In the paper, we give general parametric formulas for the fourth and fifth coefficients of functions in the Carath?odory class.

On the Correctness of Nonlinear Boundary Value Problems for Systems of Generalized Ordinary Differential Equations

1996 ◽  
Vol 3 (6) ◽  
pp. 501-524
Author(s):  
M. Ashordia
Keyword(s):  
Bounded Variation ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Continuous Operator ◽  
Functions Of Bounded Variation ◽  
Nonlinear Boundary Value Problems ◽  
Nonlinear Boundary Value ◽  
Carathéodory Class ◽  
Generalized Ordinary Differential Equations

Abstract The concept of a strongly isolated solution of the nonlinear boundary value problem dx(t) = dA(t) · f (t, x(t)), h(x) = 0, is introduced, where A : [a, b] → Rn×n is a matrix-function of bounded variation, f : [a, b] × Rn → Rn is a vector-function belonging to a Carathéodory class, and h is a continuous operator from the space of n-dimensional vector-functions of bounded variation into Rn . It is stated that the problems with strongly isolated solutions are correct. Sufficient conditions for the correctness of these problems are given.

Bohr theorems for slice regular functions over octonions

2020 ◽  
pp. 1-16
Author(s):  
Zhenghua Xu
Keyword(s):  
Unit Ball ◽  
Division Algebras ◽  
Coefficient Estimate ◽  
Coefficient Estimates ◽  
Covering Theorem ◽  
Slice Regular Functions ◽  
Regular Functions ◽  
Carathéodory Class

In this paper, we mainly investigate two versions of the Bohr theorem for slice regular functions over the largest alternative division algebras of octonions $\mathbb {O}$ . To this end, we establish the coefficient estimates for self-maps of the unit ball of $\mathbb {O}$ and the Carathéodory class in this setting. As a further application of the coefficient estimate, the 1/2-covering theorem is also proven for slice regular functions with convex image.

Conditions of the Existence and Uniqueness of Solutions of the Multipoint Boundary Value Problem for A System of Generalized Ordinary Differential Equations

1998 ◽  
Vol 5 (1) ◽  
pp. 1-24
Author(s):  
M. Ashordia
Keyword(s):  
Boundary Value Problem ◽  
Bounded Variation ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Functions Of Bounded Variation ◽  
Uniqueness Of Solutions ◽  
Continuous Functionals ◽  
Carathéodory Class ◽  
Generalized Ordinary Differential Equations ◽  
Multipoint Boundary Value Problem

Abstract Effective sufficient conditions are established for the solvability and unique solvability of the boundary value problem dx (t) = dA(t) · f(t, x(t)), xi (ti ) = ϕi (x) (i = 1, . . . , n), where , A : [a, b] → Rn×n is a matrix-function with bounded variation components, f : [a; b] × Rn → Rn is a vector-function belonging to the Carathéodory class corresponding to A; t 1, . . . , tn ∈ [a, b] and ϕ 1, . . . , ϕn are the continuous functionals (in general nonlinear) defined on the set of all vector-functions of bounded variation.

scholarly journals On weighted compositions preserving the Carathéodory class

2017 ◽  
Vol 187 (3) ◽  
pp. 459-477
Author(s):  
Irina Arévalo ◽  
Rodrigo Hernández ◽  
María J. Martín ◽  
Dragan Vukotić
Keyword(s):  
Carathéodory Class
Sign in / Sign up

Export Citation Format

Share Document