Some Properties of Analytic and P-Valent Functions Involving Certain Convolution Operators

Yakubu Gambo; Kunle Oladeji Babalola; Adamu Umar Mustapha; Daniel Eneojo Emmanuel

doi:https://doi.org/10.14445/22315373/IJMTT-V67I10P503

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 67 | Issue 10 | Year 2021 | Article Id. IJMTT-V67I10P503 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I10P503

Some Properties of Analytic and P-Valent Functions Involving Certain Convolution Operators

Yakubu Gambo, Kunle Oladeji Babalola, Adamu Umar Mustapha, Daniel Eneojo Emmanuel

Abstract

Let A(p) be denote the class of functions that are analytic in the unit disk E which have the form; f(z) = zp +ap+1 zp+1 + ap+2 zp+2 + ap+3zp+3 +.... the class of functions satisfying the geometric condition Re{ (Mnσ,p f(z)) / zp } >β was defined where, Mnσ,p : A(p) -> A(p) is an operator define using convolution * The main concern of this work is to obtain some basic properties of the class with geometric condition above. These properties include; Inclusion, Growth, and Covering theorem.

Keywords

Convolution operators, analytic and p-valent functions.

References

[1] Babalola, K. O., & Opoola, T. O. (2006). Iterated integral transforms of Caratheodory functions and their applications to analytic and univalent functions. Tamkang Journal of Mathematics, 37(4), 355-366.
[2] Babalola, K. O., (2008). New subclasses of analytic and univalent functions involving certain convolution operators. Mathematica Tome, 50(73), 3-12.
[3] Goel, R. M., & Sohi, N. S. (1980). Subclasses of univalent functions. Tamkang. J.. Math. 77-81.
[4] Noor, K.I. (1998). On an integral operator, J. Nat. Geometry, 13 (2), 127200.
[5] Noor, K. I. (2005). Generalized integral operator and multivalent functions. J. Inequal. Pure Appl. Math, 6, 1-7.
[6] Noor, K. I. (2004). Some classes of p-valent analytic functions defined by certain integral operator. Applied Mathematics and Computation, 157(3), 835-840.
[7] Pommerenke, Ch., Univalent functions, Springer-Verlag, New York Inc., 1983.
[8] Ruscheweyh, S. (1975). New criteria for univalent functions, Proc. Amer. Math. Soc., 49(1), 109115.

Citation :

Yakubu Gambo, Kunle Oladeji Babalola, Adamu Umar Mustapha, Daniel Eneojo Emmanuel, "Some Properties of Analytic and P-Valent Functions Involving Certain Convolution Operators," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 10, pp. 34-40, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I10P503