The projection on the base plane of a regular minimal surface S in R with isothermal parameters defines a complex-valued univalent harmonic function f = h(z) + g(z). The aim of this paper is to obtain the distortion inequalities for the Weierstrass-Enneper parameters of the minimal surface for the harmonic multivalent functions for which analytic part is an m-valent convex function. 2000 Mathem...

Using the integral operator, we define and study a generalized family of complex-valued harmonic functions that are univalent, sense-preserving and are associated with uniformly harmonic functions in the unit disk. We obtain coefficient inequalities, extreme points and distortion bounds for the functions in our class. The results obtained for the our class reduce to the corresponding results fo...

The purpose of this paper is to apply Wright generalized hypergeometric (Wgh) functions in defining a linear operator and obtain some inclusion relationships between the classes of harmonic univalent functions under this linear operator whenever certain Wgh inequalities with its validity conditions hold. Results for special cases of Wgh functions are also mentioned. 2000 Mathematics Subject Cla...

Inequalities involving multipliers using the sequences {cn} and {dn} of positive real numbers are introduced for complex-valued harmonic univalent functions. By specializing {cn} and {dn}, we determine representation theorems, distortion bounds, convolutions, convex combinations, and neighbourhoods for such functions. The theorems presented, in many cases, confirm or generalize various well-kno...

where h and g are analytic in D. We call h the analytic part and g the coanalytic part of f . A necessary and sufficient condition for f to be locally univalent and sense preserving in D is that |h z | > |g z | for all z in D see 1 . Let H be the class of functions of the form 1.1 that are harmonic univalent and sense preserving in the unit disk U {z : |z| < 1} for which f 0 fz 0 − 1 0. Then fo...

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...