The Boolean-algebraic structure of the so-called Schwarzian derivative is investigated. A sufficient condition for a function of several variables to behave chaotically, which concerns its associated Schwarzian derivative, ...

Let A be the class of functions f (z) of the form f (z) = z + Sigma(infinity)(k=2), a(k)z(k) that are analytic in the open unit disk D = {(z) epsilon C | |z| < 1} in 1959, K. Sakaguchi [9] has considered the subclass of A ...

The dynamic behaviour of the one-dimensional family of maps f(x) = c(2)[(a - 1)x + c(1)](-lambda/(alpha-1)) is examined, for representative values of the control parameters a, c(1), c(2) and lambda. The maps under consideration ...

Let f = h(z) + <(g(z))over bar> be a univalent sense-preserving harmonic mapping of the unit disc D = {z is an element of C parallel to z vertical bar < 1}. If f satisfies the condition vertical bar w(z)vertical bar = ...

Let V(k) be the class of functions with bounded boundary rotation and let S-H be the class of sense-preserving harmonic mappings. In the present paper we investigate a certain class of harmonic mappings related to the ...

Let f(z) = h(z) + <(g(z))over bar> be a univalent sense-preserving harmonic mapping of the open unit disc D = {z vertical bar vertical bar z vertical bar < 1}. If f satisfies the condition vertical bar omega(z)vertical ...

The main purpose of this note is tö give a new characterization for convex functions of complex order b. It should be noticed that by giving specific values to b we obtain new characterizations of important subclasses of ...

The Schwarzian derivative of a function which is defined in the interval having higher order derivatives is given by A sufficient condition for a function to behave chaotically is that its Schwarzian derivative is ...

For analytic function f(z) = z + a2z 2 + · · · in the open unit disc D, a new fractional operator Dλf(z) is defined. Applying this fractional operator Dλf(z) and the principle of subordination, we give new proofs for ...