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Estimates on the initial coefficients are obtained for normalized analytic functions f in the open unit disk with f and its inverse g = f −1 satisfying the conditions that zf ′ (z)/f (z) and zg ′ (z)/g(z) are both subordinate to a starlike univalent function whose range is symmetric with respect to the real axis. Several related classes of functions are(More)
The estimates for the second Hankel determinant a 2 a 4 – a 2 3 of the analytic function f (z) = z + a 2 z 2 + a 3 z 3 + · · · , for which either zf (z)/f (z) or 1 + zf (z)/f (z) is subordinate to a certain analytic function, are investigated. The estimates for the Hankel determinant for two other classes are also obtained. In particular, the estimates for(More)
A new theoretical model of grammatical picture generation called extended 2D context-free picture grammar (E2DCFPG) generating rectangular picture arrays of symbols is introduced. This model which allows variables in the grammar and uses the squeezing mechanism of forming the picture language over terminal symbols, is an extension of the pure 2D(More)
Motivated by the structure and functioning of the livingcell, a new computing model, called P System, was proposedin the area of Membrane Computing. Among severalareas of application of P systems, one area is concernedwith generation of picture array languages. Ceterchiet al. [1] initially proposed array-rewriting P systemsby extending the notion of(More)
and Applied Analysis 3 In the following sequel, we will assume that h is an analytic convex function inUwith h 0 1. For α ≥ γ ≥ 0, consider the third-order differential equation f ′ z αzf ′′ z γz2f ′′′ z g z , g z ≺ h z . 2.2 We will denote the class consisting of all solutions f ∈ A as R α, γ, h , that is, R ( α, γ, h ) { f ∈ A : f ′ z αzf ′′ z γz2f ′′′ z(More)
In membrane computing, P system has proved to be a rich framework for handling a variety of problems arising in different areas. In this note we examine an array-rewriting P system for rectangular picture array generation. This system makes use of Pure 2D context-free grammar rules in its regions. We obtain certain comparison results that bring out the(More)
In this paper, some subclasses of meromorphic univalent functions in the unit disk ∆ are extended. Let U (p) denote the class of normalized univa-lent meromorphic functions f in ∆ with a simple pole at z = p > 0. Let φ be a function with positive real part on ∆ with φ(0) = 1, φ (0) > 0 which maps ∆ onto a region starlike with respect to 1 which is symmetric(More)
and Applied Analysis 3 Theorem 1.3 see 12 . Let c2k c2k 1 μ k/k!, μ ∈ 0, 1 . For any positive integer n and 0 < θ < π , then i ∑n k 0 ck cos kθ > 0 if and only if 0 < μ ≤ μ0, ii ∑2n 1 k 1 ck sin kθ > 0 if and only if 0 < μ ≤ μ0, iii ∑2n k 1 ck sin kθ > 0 if 0 < μ ≤ 1/2. Here μ0 0.691556 · · · is the unique root in 0, 1 of ∫3π/2 0 cos t t1−μ dt 0. 1.6 2.(More)