Papers by Trailokya Panigrahi
In this paper, the authors introduce certain new subclasses of meromor-phic functions with a fixe... more In this paper, the authors introduce certain new subclasses of meromor-phic functions with a fixed point ξ defined in the punctured unit disk U * ξ := {z ∈ C : 0 < |z − ξ| < 1} and obtain the sharp upper bound for the coefficient functional |a 1 − µa 2 0 | for the function in this class with respect to fixed residue d. Our result generalizes the result of Ayta¸sAyta¸s and Güney (2013).
Applied Mathematics Letters, 2009
Here we investigate a majorization problem involving starlike function of complex order belonging... more Here we investigate a majorization problem involving starlike function of complex order belonging to a certain class defined by means of fractional derivatives. Relevant connections of the main results obtained in this paper with those given by earlier workers on the subject are also pointed out.
The problem of estimating coe¢ cient di¤erences for the subclass C S of convex functions appears ... more The problem of estimating coe¢ cient di¤erences for the subclass C S of convex functions appears not to have been considered. The method of [11] seems not to be applicable to C: The object of the present paper is to give sharp estimates for the di¤erence of coe¢ cients of the univalent functions de…ned in the unit disk U.
In this paper, the author introduces a new class S * λ,µ (m, s, α; η) of analytic functions which... more In this paper, the author introduces a new class S * λ,µ (m, s, α; η) of analytic functions which is defined by means of operators K m,s λ,µ,α in the open unit disk U. The operator K m,s λ,µ,α is defined as the iterations of simple form of differential and integral operators. By using well known lemma and identity, the sufficient conditions for an analytic function f to be member of the class S * λ,µ (m, s, α; η) is obtained. Several corollaries of the main result are also pointed out. The concluding section describe the possibility of further extension of the present work to p-valent functions.
In the present paper, the author investigates some subordination and superordination -preserving ... more In the present paper, the author investigates some subordination and superordination -preserving properties for analytic functions associated with generalized multiplier transformations defined on the space of normalized analytic functions in the open unit disk U. Several Sandwich-type results associated with this transformations is also derived.
International Journal of Analysis and Applications, 2016
The object of the present paper is to give some characterizations for hypergeometric distribution... more The object of the present paper is to give some characterizations for hypergeometric distribution series to be in various subclasses of analytic functions.
In this paper, we investigate some mapping properties of two new subclasses of analytic function ... more In this paper, we investigate some mapping properties of two new subclasses of analytic function classes Rk(�;b) and Vk(�;b) under generalized integral operator. Several (known or new) consequences of the results are also pointed out.
The object of this paper is to use Toeplitz determinant to obtain a sharp upper bound of the seco... more The object of this paper is to use Toeplitz determinant to obtain a sharp upper bound of the second Hankel determinant |ap+1ap+3 − ap+2| for the p-valent functions belonging to class Mp(α, β). Our main theorem unify and extend several results established earlier for special values of the parameters p, α and β.
In the present investigation we use the Jackson (p,q)-differential operator to introduce the exte... more In the present investigation we use the Jackson (p,q)-differential operator to introduce the extended Salagean operator denoted by Rkp,q. Certain bi-univalent function classes based on operator Rkp,q related to the Chebyshev polynomials are introduced. First, two coefficient bounds and Fekete-Szego inequalities for the function classes are established. A number of corollaries are developed by varying parameters involved.
Fekete–Szegö coefficient functional for quasi-subordination class
Afrika Matematika
In the present paper, we introduce a certain subclass of analytic univalent functions which is de... more In the present paper, we introduce a certain subclass of analytic univalent functions which is defined in terms of a quasi-subordination and we obtain certain sharp bounds of the Fekete–Szegö functional for functions belonging to this class. The results presented give improved versions for this and associated classes involving the subordination and majorization. Special cases of the main results are also mentioned briefly.
Let ∑ p denote the class of meromorphically multivalent functions f(z) of the form: f(z) = 1 zp +... more Let ∑ p denote the class of meromorphically multivalent functions f(z) of the form: f(z) = 1 zp + ∞ ∑ k=1 ak−pz k−p (p ∈ N := {1, 2, 3, · · · }) which are analytic in the punctured open unit disk U∗ = {z : 0 < |z| < 1}. In this paper, by making use of a meromorphic analogue of the Cho-Kwon-Srivastava operator and its iterations, a new subclass of meromorphic p-valent functions is introduced. Inclusion theorems and other properties of these function class are studied.
Journal of the Korean Mathematical Society
In this paper, subordination results of analytic function f ∈ Ap involving linear operator K δ,λ ... more In this paper, subordination results of analytic function f ∈ Ap involving linear operator K δ,λ c,p are obtained. By applying the differential subordination method, results are derived under some sufficient subordination conditions. On using some hypergeometric identities, corollaries of the main results are derived. Furthermore, convolution preserving properties for a class of multivalent analytic function associated with the operator K δ,λ c,p are investigated.
In this paper, the authors obtain an upper bound of second Hankel determinant for a new class of ... more In this paper, the authors obtain an upper bound of second Hankel determinant for a new class of analytic functions defined through the Komatu integral operator. Our result extends the corresponding previously known results.
Studia Universitatis Babes-Bolyai Matematica
In the present paper, the authors introduce a generalized Sakaguchi type non-Bazilevic function c... more In the present paper, the authors introduce a generalized Sakaguchi type non-Bazilevic function class M λ,β q (φ, s, t) of analytic functions involving quasi-subordination and obtain bounds for the Fekete-Szegö functional |a3 − µa 2 2 | for the functions belonging to the above and associated classes. Some important and useful special cases of the main results are also pointed out.
Proyecciones (Antofagasta)
Boletim da Sociedade Paranaense de Matemática
In this paper, a new subclass of analytic functions ML_{\lambda}^{*} associated with the right h... more In this paper, a new subclass of analytic functions ML_{\lambda}^{*} associated with the right half of the lemniscate of Bernoulli is introduced. The sharp upper bound for the Fekete-Szego functional |a_{3}-\mu a_{2}^{2}| for both real and complex \mu are considered. Further, the sharp upper bound to the second Hankel determinant |H_{2}(1)| for the function f in the class ML_{\lambda}^{*} using Toeplitz determinant is studied. Relevances of the main results are also briefly indicated.
Studia Universitatis Babes-Bolyai Matematica
In the present paper, by considering suitable classes of admissible functions we investigate some... more In the present paper, by considering suitable classes of admissible functions we investigate some strong differential subordination as well as superordination results for analytic functions associated with normalized form of the generalized Struve functions. As a consequence of these results, new strong differential sandwich-type results are obtained.
Bulletin of the Korean Mathematical Society
In the present investigation, the author introduces two interesting subclasses of normalized mero... more In the present investigation, the author introduces two interesting subclasses of normalized meromorphic univalent functions w = f (z) defined on∆ := {z ∈ C : 1 < |z| < ∞} whose inverse f −1 (w) is also univalent meromorphic in∆. Estimates for the initial coefficients are obtained for the functions in these new subclasses.
Studia Universitatis Babes-Bolyai Matematica
In this paper, the authors introduce a new general integral operator for multivalent functions. T... more In this paper, the authors introduce a new general integral operator for multivalent functions. The new sufficient conditions for the operator J α i , β i p,γ,g (f1, f2, ..., fn) when γ = 1 is determined for the class of p-valently starlike, p-valently close-to-convex, uniformly p-valent close-to-convex and strongly starlike of order δ (0 < δ ≤ 1) in U. Our results generalize the results of Frasin [7].
Boletim da Sociedade Paranaense de Matemática
In this paper, the authors introduce a generalized Sakaguchi type spiral-likefunction class S(\la... more In this paper, the authors introduce a generalized Sakaguchi type spiral-likefunction class S(\lambda, \beta, s, t) and obtain sharp upper bound to thesecond Hankel determinant |H_{2}(1)| for the function f in the above class.Relevances of the main result are also briefly indicated.
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Papers by Trailokya Panigrahi