arXiv subjects
Publications and source records attributed to Halit Orhan.
In the present investigation, we consider two new subclasses N_{Σ}^{μ}(α,λ) and N_{Σ}^{μ}(β,λ) of bi-univalent functions defined in the open unit disk U={z:|z|<1}. Besides, we find upper bounds for the second and third coefficients for functions in these new subclasses.
In this paper we obtain, by the method of Loewner chains, some sufficient conditions for the analyticity and the univalence of the functions defined by an integral operator. These conditions in- volves Ruscheweyh and Salagean derivative operator in the open unit disk. In particular cases, we find the well-known conditions for univalency established by Becker [3], Ahlfors [2], Kanas and Srivastava [8] and others for analytic mappings f : U ! C: Also, we obtain the corresponding new, useful and simpler conditions for this integral operator.
The object of the present paper is to obtain a more general condition for univalence of meromorphic functions in the U*. The significant relationships and relevance with other results are also given. A number of known univalent conditions would follow upon specializing the parameters involved in our main results.
In this paper we introduce and study two new subclasses Σ_{λμ mp}(α,β)$ and $Σ^{+}_{λμmp}(α,β)$ of meromorphically multivalent functions which are defined by means of a new differential operator. Some results connected to subordination properties, coefficient estimates, convolution properties, integral representation, distortion theorems are obtained. We also extend the familiar concept of $% (n,δ)-$neighborhoods of analytic functions to these subclasses of meromorphically multivalent functions.
In the present paper the new multiplier transformations $\mathrm{{\mathcal{J}% }}_{p}^{δ}(λ,μ,l)$ $(δ,l\geq 0,\;λ\geq μ\geq 0;\;p\in \mathrm{% }%\mathbb{N} )}$ of multivalent functions is defined. Making use of the operator $\mathrm{% {\mathcal{J}}}_{p}^{δ}(λ,μ,l),$ two new subclasses $\mathcal{% P}_{λ,μ,l}^{δ}(A,B;σ,p)$ and $\widetilde{\mathcal{P}}% _{λ,μ,l}^{δ}(A,B;σ,p)$\textbf{\ }of multivalent analytic functions are introduced and investigated in the open unit disk. Some interesting relations and characteristics such as inclusion relationships, neighborhoods, partial sums, some applications of fractional calculus and quasi-convolution properties of functions belonging to each of these subclasses $\mathcal{P}_{λ,μ,l}^{δ}(A,B;σ,p)$ and $\widetilde{\mathcal{P}}_{λ,μ,l}^{δ}(A,B;σ,p)$ are investigated. Relevant connections of the definitions and results presented in this paper with those obtained in several earlier works on the subject are also pointed out.