We introduce a class TS p(α) of analytic functions with negative coefficients defined by convolution with a fixed analytic function g(z) = z+ P∞ n=2 bnz , bn > 0, |z| < 1. We obtain the coefficient inequality, coefficient estimate, distortion theorem, a convolution result, extreme points and integral representation for functions in the class TS p(α).

Necessary and sufficient coefficient bounds and convolution condition for certain multivalent harmonic functions whose convolution with generalized hypergeometric functions is starlike of order γ are investigated. Results on extreme points, convex combination and distortion bounds using the coefficient condition are also obtained. 2010 Mathematics Subject Classification: 30C45, 30C50

In the present paper we study convolution properties for subclasses of univalent harmonic functions in the open unit disc and obtain some basic properties such as coefficient characterization and extreme points.  

in the present paper we study convolution properties for subclasses of univalent harmonic functions in the open unit disc and obtain some basic properties such as coefficient characterization and extreme points.

Ruscheweyh‘and She&Small proved the P6lya-Schoenberg conjecture that the class of convex analytic functions is closed under convolution or Hadamard product. They also showed that clos&o-convexity is preserved under convolution with convex analytic functions. In this note, we investigate harmonic analogs. Beginning with convex analytic functions, we form certain harmonic functions which preserve...

Any monotone Boolean circuit computing the n-dimensional Boolean convolution requires at least n2 and-gates. This matches the obvious upper bound. The previous best bound for this problem was Ω(n4/3), obtained by Norbert Blum in 1981. More generally, exact bounds are given for all semi-disjoint bilinear forms.

A quasi-polynomial is a function defined of the form q(k) = c d (k) k d + c d−1 (k) k d−1 + · · · + c0(k), where c0, c1,. .. , c d are periodic functions in k ∈ Z. Prominent examples of quasi-polynomials appear in Ehrhart's theory as integer-point counting functions for rational polytopes, and McMullen gives upper bounds for the periods of the cj (k) for Ehrhart quasi-polynomials. For generic p...

A quasi-polynomial is a function defined of the form q(k) = c d (k) k d + c d−1 (k) k d−1 + · · · + c0(k), where c0, c1,. .. , c d are periodic functions in k ∈ Z. Prominent examples of quasi-polynomials appear in Ehrhart's theory as integer-point counting functions for rational polytopes, and McMullen gives upper bounds for the periods of the cj (k) for Ehrhart quasi-polynomials. For generic p...

Sufficient coefficient conditions for complex functions to be close-to-convex harmonic or convex harmonic are given. Construction of close-to-convex harmonic functions is also studied by looking at transforms of convex analytic functions. Finally, a convolution property for harmonic functions is discussed. Harmonic, Convex, Close-to-Convex, Univalent.

The wave equation occurs in many branches of physics, in applied mathematics as well as in engineering, and it is also considered as one of the three fundamental equations in mathematical physics. The homogenous wave equation with constant coefficient can be solved by many ways such as separation of variables [1], the methods of characteristics [2, 3], and Laplace transform and Fourier transfor...