We present a comparative study of four product operators on weighted languages: (i) the convolution, (ii) the shuffle, (iii) the infiltration, and (iv) the Hadamard product. Exploiting the fact that the set of weighted languages is a final coalgebra, we use coinduction to prove that a classical operator from difference calculus in mathematics: the Newton transform, generalises (from infinite se...

In this paper, we introduce two subclasses Ωp(α) and Λ ∗ p(α) of meromorphic pvalent functions in the punctured diskD = {z : 0 < |z| < 1}. Coefficient inequalities, distortion theorems, the radii of starlikeness and convexity, closure theorems and Hadamard product ( or convolution) of functions belonging to these classes are obtained.

Making use a linear operator, which is defined here by means of the Hadamard product (or convolution) involving the generalized hypergeometric function, we introduce two novel subclasses Qp,q,s(α1;A,B,λ) and Qp,q,s(α1;A,B,λ) of meromorphically multivalent functions of order λ (0 λ < p) in the punctured disc U∗ . In this paper we investigate the various important properties and characteristics o...

Krust established that all conjugate and associate surfaces of a minimal graph over a convex domain are also graphs. Using a convolution theorem from the theory of harmonic univalent mappings, we generalize Krust’s theorem to include the family of convolution surfaces which are generated by taking the Hadamard product or convolution of mappings. Since this convolution involves convex univalent ...

This paper aims to provide sufficient conditions for starlikeness and convexity of Hadamard product (convolution) certain multivalent analytic functions with positive real parts. Moreover, the a integral operator other convolution results are also considered.

We define new classes of the family E(Φ,Ψ), in a unit disk U := {z ∈ C, |z| < 1}, as follows: for analytic functions F (z),Φ(z) and Ψ(z) so that <{ (z)∗Φ(z) F (z)∗Ψ(z)} > 0, z ∈ U, F (z) ∗Ψ(z) 6= 0 where the operator ∗ denotes the convolution or Hadamard product. Moreover, we establish some subordination results for these new classes.

Using convolution (or Hadamard product), we define the El-Ashwah and Drbuk linear operator, which is a multivalent function in unit disk U=w:w&lt;1 w∈₵, satisfy its specific relationship to derive subordination, superordination, sandwich results for this operator by using properties of subordination superordination concepts.

"Making use of a modi ed Hadamard product or convolution harmonic functions with varying arguments, combined an integral operator, we study when these belong to given class. Following idea U. Bednarz and J. Sokol de ne the order consistence three classes determine it for certain arguments ned using operator."

Keywords: Analytic functions Multivalent prestarlike function Linear operator Hadamard product Subordination a b s t r a c t In the paper we introduce general classes of multivalent analytic functions defined by the subordination. In particular, we define the class of multivalent prestarlike functions. By using the Ruscheweyh's duality theory we investigate convolution properties related to mul...