scholarly journals A Picard type theorem concerning meromorphic functions of\\ hyper-order

2016 ◽  
Vol 47 (3) ◽  
pp. 357-370 ◽  
Author(s):  
PANG XueCheng ◽  
YANG Pai ◽  
NIU PeiYan
Keyword(s):  
Meromorphic Functions ◽  
Type Theorem ◽  
Hyper Order ◽  
Picard Type Theorem

scholarly journals On Existence Theorems to Symmetric Functional Set-Valued Differential Equations

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1219
Author(s):  
Marek T. Malinowski
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Existence Theorems ◽  
Type Theorem ◽  
Integral Representations ◽  
Uniqueness Of The Solution ◽  
Nonempty Compact ◽  
Picard Type Theorem ◽  
Convex Subsets

In this paper, we consider functional set-valued differential equations in their integral representations that possess integrals symmetrically on both sides of the equations. The solutions have values that are the nonempty compact and convex subsets. The main results contain a Peano type theorem on the existence of the solution and a Picard type theorem on the existence and uniqueness of the solution to such equations. The proofs are based on sequences of approximations that are constructed with appropriate Hukuhara differences of sets. An estimate of the magnitude of the solution’s values is provided as well. We show the closeness of the unique solutions when the equations differ slightly.

scholarly journals A Class of Nonlinear Integral Operators Preserving Double Subordinations

2008 ◽  
Vol 2008 ◽  
pp. 1-10 ◽  
Author(s):  
Oh Sang Kwon ◽  
Nak Eun Cho
Keyword(s):  
Unit Disk ◽  
Meromorphic Functions ◽  
Type Theorem ◽  
Integral Operators ◽  
Open Unit ◽  
Open Unit Disk ◽  
Sandwich Type ◽  
Space Of Meromorphic Functions ◽  
Nonlinear Integral Operators

The purpose of the present paper is to investigate some subordination- and superordination-preserving properties of certain integral operators defined on the space of meromorphic functions in the punctured open unit disk. The sandwich-type theorem for these integral operators is also considered.

Uniqueness and periodicity for meromorphic functions with partial sharing values

2019 ◽  
Vol 69 (1) ◽  
pp. 99-110
Author(s):  
Weichuan Lin ◽  
Shengjiang Chen ◽  
Xiaoman Gao
Keyword(s):  
Uniqueness Theorem ◽  
Meromorphic Functions ◽  
Sharing Values ◽  
Hyper Order

Abstract We prove a periodic theorem of meromorphic functions of hyper-order ρ2(f) < 1. As an application, we obtain the corresponding uniqueness theorem on periodic meromorphic functions. In addition, we show the accuracy of the results by giving some examples.

scholarly journals Holomorphic mappings into the complex projective space with moving hypersurfaces

Filomat ◽  
2021 ◽  
Vol 35 (3) ◽  
pp. 955-962
Author(s):  
Liu Yang
Keyword(s):  
Projective Space ◽  
Recent Work ◽  
General Position ◽  
Complex Projective Space ◽  
Type Theorem ◽  
Complex Variables ◽  
Holomorphic Mappings ◽  
Several Complex Variables ◽  
Picard Type Theorem ◽  
Complex Projective

Motivated by Eremenko?s accomplisshment of a Picard-type theorem [Period Math Hung. 38 (1999), pp.39-42.], we study the normality of families of holomorphic mappings of several complex variables into PN(C) for moving hypersurfaces located in general position. Our results generalize and complete previous results in this area, especially the works of Dufresnoy, Tu-Li, Tu-Cao, Yang-Fang-Pang and the recent work of Ye-Shi-Pang.

scholarly journals A note on power of meromorphic function and its shift operator of certain hyper-order sharing one small function and a value

2021 ◽  
Vol 55 (1) ◽  
pp. 57-63
Author(s):  
A. Banerjee ◽  
A. Roy
Keyword(s):  
Meromorphic Function ◽  
Meromorphic Functions ◽  
Shift Operator ◽  
Small Function ◽  
A Value ◽  
Hyper Order

In this article, we obtain two results on $n$ the power of a meromorphic function and its shift operator sharing a small function together with a value which improve and complement some earlier results. In particular, more or less we have improved and extended two results of Qi-Yang [Meromorphic functions that share values with their shifts or their $n$-th order differences, Analysis Math., 46(4)2020, 843-865] by dispelling the superfluous conclusions in them.

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