On the generalized Roper-Suffridge extension operator in Banach spaces
نویسندگان
چکیده
The generalized Roper-Suffridge extension operator in Banach spaces is introduced. We prove that this operator preserves the starlikeness on some domains in Banach spaces and does not preserve convexity in some cases. Furthermore, the growth theorem and covering theorem of the corresponding mappings are given. Some results of Roper and Suffridge and Graham et al. in Cn are extended to Banach spaces.
منابع مشابه
THE ROPER-SUFFRIDGE EXTENSION OPERATORS ON THE CLASS OF STRONG AND ALMOST SPIRALLIKE MAPPINGS OF TYPE $beta$ AND ORDER $alpha$
Let$mathbb{C}^n$ be the space of $n$ complex variables. Let$Omega_{n,p_2,ldots,p_n}$ be a complete Reinhardt on$mathbb{C}^n$. The Minkowski functional on complete Reinhardt$Omega_{n,p_2,ldots,p_n}$ is denoted by $rho(z)$. The concept ofspirallike mapping of type $beta$ and order $alpha$ is defined.So, the concept of the strong and almost spirallike mappings o...
متن کاملParabolic starlike mappings of the unit ball $B^n$
Let $f$ be a locally univalent function on the unit disk $U$. We consider the normalized extensions of $f$ to the Euclidean unit ball $B^nsubseteqmathbb{C}^n$ given by $$Phi_{n,gamma}(f)(z)=left(f(z_1),(f'(z_1))^gammahat{z}right),$$ where $gammain[0,1/2]$, $z=(z_1,hat{z})in B^n$ and $$Psi_{n,beta}(f)(z)=left(f(z_1),(frac{f(z_1)}{z_1})^betahat{z}right),$$ in which $betain[0,1]$, $f(z_1)neq 0$ a...
متن کاملOn some fixed points properties and convergence theorems for a Banach operator in hyperbolic spaces
In this paper, we prove some fixed points properties and demiclosedness principle for a Banach operator in uniformly convex hyperbolic spaces. We further propose an iterative scheme for approximating a fixed point of a Banach operator and establish some strong and $Delta$-convergence theorems for such operator in the frame work of uniformly convex hyperbolic spaces. The results obtained in this...
متن کاملA New Roper-Suffridge Extension Operator on a Reinhardt Domain
and Applied Analysis 3 In contrast to the modified Roper-Suffridge extension operator in the unit ball, it is natural to ask if we can modify the Roper-Suffridge extension operator on the Reinhardt domains. In this paper, we will introduce the following modified operator: F z ⎛ ⎝f z1 f ′ z1 n ∑ j 2 ajz pj j , ( f ′ z1 2z2, . . . , ( f ′ z1 nzn ⎞ ⎠ ′ 1.5 on the Reinhardt domainΩn,p2,...,pn . Wew...
متن کاملA SYSTEM OF GENERALIZED VARIATIONAL INCLUSIONS INVOLVING G-eta-MONOTONE MAPPINGS
We introduce a new concept of general $G$-$eta$-monotone operator generalizing the general $(H,eta)$-monotone operator cite{arvar2, arvar1}, general $H-$ monotone operator cite{xiahuang} in Banach spaces, and also generalizing $G$-$eta$-monotone operator cite{zhang}, $(A, eta)$-monotone operator cite{verma2}, $A$-monotone operator cite{verma0}, $(H, eta)$-monotone operator cite{fanghuang}...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Int. J. Math. Mathematical Sciences
دوره 2005 شماره
صفحات -
تاریخ انتشار 2005