The generalized Roper–Suffridge extension operator for some biholomorphic mappings

On the generalized Roper-Suffridge extension operator in Banach spaces

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 sp...

Kernel Convergence and Biholomorphic Mappings in Several Complex Variables

We deal with kernel convergence of domains in Cn which are biholomorphically equivalent to the unit ball B. We also prove that there is an equivalence between the convergence on compact sets of biholomorphic mappings on B, which satisfy a growth theorem, and the kernel convergence. Moreover, we obtain certain consequences of this equivalence in the study of Loewner chains and of starlike and co...

EXTENSION OF FUZZY CONTRACTION MAPPINGS

In a fuzzy metric space (X;M; *), where * is a continuous t-norm,a locally fuzzy contraction mapping is de ned. It is proved that any locally fuzzy contraction mapping is a global fuzzy contractive. Also, if f satis es the locally fuzzy contractivity condition then it satis es the global fuzzy contrac-tivity condition.    

Some Subclasses of Analytic Functions Defined by Generalized Differential Operator

Let A denote the class of analytic functions in the open unit disk U = {z : |z| < 1} normalized by f(0) = f ′(0) − 1 = 0. In this paper, we introduce and study certain subclasses of analytic functions. Several inclusion relations of various subclasses of analytic functions, coefficient estimates , growth and distortion theorems, Hadamard Product, extreme points, integral means and inclusion pro...

An Operator Extension of Bohr's inequality