which are analytic in the open unit disk E. Also, A1 = A, the usual class of analytic functions defined in the open unit disk E = {z : |z| < 1}. Let f(z) and g(z) be analytic in E. We say that the function f is subordinate to the function g and write f(z) ≺ g(z), if and only if there exists Schwarz function w, analytic in E such that w(0) = 0, |w(z)| < 1 for z ∈ E, and f(z) = g(w(z)). In partic...

An analytic hypersurface of M is a subset V ⊂ M such that for each point x ∈ V there exists an open set Ux ⊂ M containing x and a holomorphic function fx defined on Ux such that V ⊂ Ux is the zero-set of fx. Such an fx is called a local defining function for V near x. The quotient of any two local defining functions around x is a non-vanishing holomorphic function around x. An analytic hypersur...

Making use of the familiar convolution structure of analytic functions, in this paper we introduce and investigate two new subclasses of multivalently analytic functions of complex order. Among the various results obtained here for each of these function classes, we derive the coefficient bounds and coefficient inequalities, and inclusion and neighborhood properties, involving multivalently ana...

The key point in this paper is the introduction of elastic analytic functions. An elastic analytic function is a function of the form u : C ! C 2 which is diierentiable and satisses equations which are analogous to the Cauchy-Riemann equations of traditional complex analysis such that the following conditions hold: rst the real and imaginary part of the rst complex component of u satisfy the Na...

\begin{abstract} Let $P\pm$ be the Riesz's projection operator and let $P_-= I - P_+$. We consider estimates of expression $\|( |P_ + f | ^s |P_- |^s) ^{\frac{1}{s}}\|_{L^p (\mathbf{T})}$ in terms Lebesgue $p$-norm function $f \in L^p(\mathbf{T})$. find accurate for $p\geq 2$ $0<s\leq p$, thus significantly improving results from \cite{KALAJ.TAMS} where it is considered $s=2$ $1<p<\infty$. Inte...

We show that the derivative of a log-analytic function is log-analytic. prove functions exhibit strong quasianalytic properties. establish parametric version Tamm’s theorem for functions.

The proof of uniqueness in a larger class of strategies closely follows McLennan et al. (2014) Theorem 1.2, which proves uniqueness in the one-shot Kyle (1985) model. Complex-variable functions are used, so more definitions are needed. A real entire function is smooth and coincides on R with its Taylor series centered at zero. A region is an open connected set D ⊆ C. A function is analytic on D...

The main objective of this investigation is to introduce certain new subclasses of the class $Sigma $ of bi-univalent functions by using concept of conic domain. Furthermore, we find non-sharp estimates on the first two Taylor-Maclaurin coefficients $ left vert a_{2}right vert $ and $left vert a_{3}right vert $ for functions in these new subclasses. We consider various corollaries and consequen...

The general problem of interpolation and approximation to an arbitrary given analytic function by means of polynomials or more general rational functions, is an important one on which the existing literature is large, including a recent book by the present writer. ' Analogous to this problem is the new but related problem of interpolation and approximation to an arbitrary given analytic functio...