here, we have considered the husimi and wigner distribution functions. we have, inparticular, shown how the uncertainty principle works for the two cases of simple and damped harmonicoscillators when either of these two distributions are used. the conclusion shows that the husimidistribution function remains non-negative through the phase space but it does not always satisfies theuncertainty pr...

This is an introductory survey on applications of the Julia variation to problems in geometric function theory. A short exposition is given which develops a method for treating extremal problems over classes F of analytic functions on the unit disk D for which appropriate subsets Fn can be constructed so that (i) F = ⋃ n Fn and (ii) for each f ∈ Fn a geometric constraint will hold that ∂f(D) wi...

The main purpose of the present paper is to derive a new criterion for mul-tivalent starlike functions by applying Jack's lemma.

In 1999, for (0≤k<∞), the concept of conic domain by defining k-uniform convex functions were introduced Kanas and Wisniowska then in 2000, they defined related k-starlike denoted k−UCV k−ST respectively. Motivated their studies, our work, we define class k-parabolic starlike functions, k−SHm,q, using quasi-subordination m-fold symmetric analytic making use Ωk. We determine coefficient bound...

Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract Let U = {z ∈ C : |z| < 1} be the unit disc in the complex plane.Let Σ k be the class of meromorphic functions f in U having the form: f (z) = 1 z + α k z k + · · · , 0 < |z| < 1, k ≥ 0 A function f ∈ Σ = Σ 0 is called starlike...

In 1999, Kanas and Rønning introduced the classes of starlike and convex functions, which are normalized with f (w) = f ′(w)− 1 = 0 and w a fixed point in U . In 2005, the authors introduced the classes of functions close to convex and α-convex, which are normalized in the same way. All these definitions are somewhat similar to the ones for the uniform-type functions and it is easy to see that ...

An analytic functions f(z) defined on 4 = {z : |z| < 1} and normalized by f(0) = 0, f ′(0) = 1 is starlike with respect to conjugate points

The object of the present paper is to prove a criterion for p-valently starlike functions in the open unit disk.