**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30127

##### Geometric Properties and Neighborhood for Certain Subclasses of Multivalent Functions

**Authors:**
Hesam Mahzoon

**Abstract:**

By using the two existing operators, we have defined an operator, which is an extension for them. In this paper, first the operator is introduced. Then, using this operator, the subclasses of multivalent functions are defined. These subclasses of multivalent functions are utilized in order to obtain coefficient inequalities, extreme points, and integral means inequalities for functions belonging to these classes.

**Keywords:**
Coefficient inequalities,
extreme points,
integral means,
multivalent functions,
Al-Oboudi operator,
and Sãlãgean operator.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1132431

**References:**

[1] F. M. Al - Oboudi, On univalent functions defined by a generalized Sălă gean operator, Ind. J. Math. Math. Sci., 2004, No. 25 - 28, pp. 1429 - 1436.

[2] P. L. Duren, Univalent functions, Springer-Verlag, 1983.

[3] S. S. Eker and S. Owa, Certian classes of analytic functions involving Sălă gean operator, J. Inequal. Pure Appl. Math., (in course of publication).

[4] S. S. Eker and S. Owa, New applications of classes of analytic functions involving Sălă gean operator, International Symposium on Complex Function Theory and Applications, Brasov, Romania, 2006, pp. 1 - 5.

[5] S. S. Eker and B. Seker, On a class of multivalent functions defined by Sălă gean operator, General Mathematics, Vol. 15, Nr. 2-3, 2007, pp. 154 - 163.

[6] A. W. Goodman, Univalent functions and nonanalytic curves, Proc. Amer. Math. Soc., 8(3), 1957, pp. 598-601.

[7] M. S. Robertson, On the theory of univalent functions, Annals of Math., 37, 1936, pp. 374 - 406.

[8] S. Ruscheweyh, Neighbohoods of univalent functions, Proc. Amer. Math. Soc., 81, 1981, pp. 521-527.

[9] G. S. Sălă Gean, On some classes of univalent functions, Seminar of Geometric function theory, Cluj - Napoca, 1983.

[10] S. Shams, S. R. Kulkarni and J. M. Jahangiri, Classes of uniformly starlike and convex functions, International Journal of Mathematics and Mathematical Science, 55, 2004, pp. 2959 - 2961.