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Neighborhoods of p-valent functions
Hesam Mahzoon,S. Latha 장전수학회 2013 Proceedings of the Jangjeon mathematical society Vol.16 No.1
In this paper, we the new subclasses of p - valent functions of complexorder denoted by Hpn,m(q, λ, b), Lpn,m(q, λ, b; μ), Hp,n,m(q, λ, b) and Lp,n,a,m(q, λ, b; μ)are introduced. Further for functions belonging to these classes, certain propertiesof neighborhoods are studied.
NEIGHBORHOODS OF p -VALENT FUNCTIONS
HESAM MAHZOON,S. LATHA 장전수학회 2010 Advanced Studies in Contemporary Mathematics Vol.20 No.1
In this paper, we the new subclasses of p - valent functions of complex order denoted byHp n,m(q, ⋋, b),Lpn,m(q, ⋋,b; μ),Hp,a,n,m(q, ⋋, b) and Lp,a,n,m(q, ⋋, b; μ)are introduced. Further for functions belonging to these classes, certain properties of neighborhoods are studied
On Coefficients of a Certain Subclass of Starlike and Bi-starlike Functions
Mahzoon, Hesam,Sokol, Janusz Department of Mathematics 2021 Kyungpook mathematical journal Vol.61 No.3
In this paper we investigate a subclass 𝓜(α) of the class of starlike functions in the unit disk |z| < 1. 𝓜(α), π/2 ≤ α < π, is the set of all analytic functions f in the unit disk |z| < 1 with the normalization f(0) = f'(0) - 1 = 0 that satisfy the condition $$1+\frac{{\alpha}-{\pi}}{2\;sin\;{\alpha}}<Re\{\frac{zf^{\prime}(z)}{f(z)}\}<1+\frac{{\alpha}}{2\;sin\;{\alpha}}\;(z{\in}{\Delta})$$. The class 𝓜(α) was introduced by Kargar et al. [Complex Anal. Oper. Theory 11: 1639-1649, 2017]. In this paper some basic geometric properties of the class 𝓜(α) are investigated. Among others things, coefficients estimates and bound are given for the Fekete-Szegö functional associated with the k-th root transform [f(z<sup>k</sup>)]<sup>1/k</sup>. Also a certain subclass of bi-starlike functions is introduced and the bounds for the initial coefficients are obtained.