The main purpose of this paper is to introduce and investigate a certain subclass of meromorphic close-to-convex functions. Such results as coefficient inequalities, convolution property, inclusion relationship, distortion property, and radius of meromorphic convexity are derived.

We consider the Sakaguchi functions which are starlike with respect to symmetrical points in the open unit disk U and extend it to class SH(α, t) concerning with Sakaguchi-type complex-valued harmonic univalent functions in U. A sufficient coefficient condition and a necessary and sufficient convolution characterization for such harmonic functions are determined. In addition, by using the coeff...

Abstract -A complex-valued functions that are univalent and sense preserving in the unit disk U can be written in the form ( ) ( ) ( ) f z h z g z   , where U(z) and g(z) are analytic in. We will introduced the operator D which defined by convolution involving the polylogarithms functions. Using this operator, we introduce the class HP(,, n) by generalized derivative operator of harmonic un...

Two classes of univalent harmonic functions on unit disc satisfying the conditions ∑∞ n=2(n−α)(|an|+|bn|) ≤ (1−α)(1−|b1|) and ∑∞ n=2 n(n−α)(|an|+|bn|) ≤ (1−α)(1−|b1|) are given. That the ranges of the functions belonging to these two classes are starlike and convex, respectively. Sharp coefficient relations and distortion theorems are given for these functions. Furthermore results concerning th...

In this paper we introduce a new class H(φ, α, β) of analytic functions which is defined by means of a Hadamard product (or convolution) of two suitably normalized analytic functions. Several properties like, the coefficient bounds, growth and distortion theorems, radii of starlikeness, convexity and close-to-convexity are investigated. We further consider a subordination theorem, certain bound...

In this paper, we have discussed the meromorphic p-valent functions that satisfy the differential subordinations z(Ip(r, λ)f(z)) (Ip(r, λ)f(z))(j) ≺ (1 + A−B a βz 1 +Bz )(p+ j), z ∈ ∆, where β is complex number and Ip(r, λ) is salagean Operator. Also we study coefficient inequalities and hadamard product (convolution) and found radius of starlikeness and convexity. We investigate some interesti...

There is a wide and nearly complete theory of trigonometric series with random coefficients; on the other hand, much less is known on trigonometric series with random frequencies. In this paper we study the asymptotic behavior of SN = ∑N k=1 sinnkx for random sequences (nk)k≥1, independent and identically distributed over disjoint intervals Ik ⊂ (0,∞) of the same length. As it turns out, the be...

The purpose of the present paper is to study some results involving coefficient conditions, extreme points, distortion bounds, convolution conditions and convex combination for a new class of harmonic multivalent functions in the open unit disc. Relevant connections of the results presented here with various known results are briefly indicated.

Paul Garrett [email protected] http://www.math.umn.edu/ g̃arrett/ [This document is http://www.math.umn.edu/ ̃garrett/m/repns/notes 2014-15/03 generalities finite.pdf] 1. Subrepresentations, complete reducibility, unitarization 2. Dual/contragredient representations 3. Regular and biregular representations L(G) 4. Schur’s lemma 5. Central characters of irreducibles 6. Tensor products of repres...