SOME BAZILEVI FUNCTIONS OF ORDER BETA

Distortion theorems and coefficient estimates are obtained for a new class of Bazilevi functions.

Let S be the class of normalized functions regular and univalent in the unlt disc D z z < and S the subclass of starlike functions.
Denote by P(), the class of functions which are regular in D and such that for h P(B), h (O) and Re h(z) > 8 for z D. We write P P(O).
Bazllevlc [I] showed that the class of normalized regular functions f with representation f(z) =f p(t) g(t) = t -I dt) = (I.1), when > O, g S and p P for z D forms a subclass of S. We denote this class of functions by B().See also [2].Let > 0. Then it follows easily from (I.I) that f B() if, and only if, , there exists g S such that for z D Re z f'(z) > 0.
(1.2) fCz)-gCz) In [3], Singh considered the subclass Bl(e) of B(s) obtained by taking g(z) z in (,.4) (z) We note that BI(I,O) R, the class of functions whose derivative has real part [4].BI(I,) was considered in [5].Zamorskl [6] and Thomas [7] solved the coefficient problem for f B(), in the case when N is a positive Integer.In [7], sharp distortion theorems were obtained for f BI() for > 0. The object of this paper i5 to extend these results to the class BI(,8).The class BI(,B) has also recently been considered in [8].
where and Equality holds in all cases for the function f defined by f (z) af t 'I ((l+tei)(l-B) + B)dt) (l-te 10) where 0 or (2.1) PROOF.
(i) Since f BI(,8) and it follows from (1.4) that l-f for z D and p P.
The following shows that as a 0 the bounds In Theorem are asymptotic to the distortion theorems for starlike functions of order 8 > 0 (see eg. [9]).THEOREM 2.

Call for Papers
This subject has been extensively studied in the past years for one-, two-, and three-dimensional space.Additionally, such dynamical systems can exhibit a very important and still unexplained phenomenon, called as the Fermi acceleration phenomenon.Basically, the phenomenon of Fermi acceleration (FA) is a process in which a classical particle can acquire unbounded energy from collisions with a heavy moving wall.This phenomenon was originally proposed by Enrico Fermi in 1949 as a possible explanation of the origin of the large energies of the cosmic particles.His original model was then modified and considered under different approaches and using many versions.Moreover, applications of FA have been of a large broad interest in many different fields of science including plasma physics, astrophysics, atomic physics, optics, and time-dependent billiard problems and they are useful for controlling chaos in Engineering and dynamical systems exhibiting chaos (both conservative and dissipative chaos).
We intend to publish in this special issue papers reporting research on time-dependent billiards.The topic includes both conservative and dissipative dynamics.Papers discussing dynamical properties, statistical and mathematical results, stability investigation of the phase space structure, the phenomenon of Fermi acceleration, conditions for having suppression of Fermi acceleration, and computational and numerical methods for exploring these structures and applications are welcome.
To be acceptable for publication in the special issue of Mathematical Problems in Engineering, papers must make significant, original, and correct contributions to one or more of the topics above mentioned.Mathematical papers regarding the topics above are also welcome.
Authors should follow the Mathematical Problems in Engineering manuscript format described at http://www .hindawi.com/journals/mpe/.Prospective authors should submit an electronic copy of their complete manuscript through the journal Manuscript Tracking System at http:// mts.hindawi.com/according to the following timetable:

S
(1.2).Thus f BI() if and only if, for > 0 and z D 0 B < I, f e BI(,) If, and only if, for z