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1
Content available remote On multivalent close-to-star functions
Singh Gagandeep, Singh Gurcharanjit
Fasciculi Mathematici
|
2023
|
nr 66
91--106
EN
The present paper deals with certain generalized subclasses of multivalent close-to-star functions defined with subordination. Various properties of these classes such as the coefficient estimates, growth theorems, argument theorems and inclusion relations are studied. Some earlier known results will follow as particular cases.
2
Extensions of coefficient estimates for new classes of bi-univalent functions defined by Sălăgean integro-differential operator
Páll-Szabó Ágnes Orsolya
Journal of Applied Analysis
|
2021
|
Vol. 27, nr 1
87--95
EN
In this paper, we introduce and investigate three new general classes of bi-starlike and bi-convex functions of Ma-Minda type defined by the Sălăgean integro-differential operator. Bounds of the first three coefficients |a2|, |a3| and |a4| are given.
3
Some sufficient conditions for univalence and close-to-convexity
Nunokawa Mamoru, Cho Nak Eun, Kwon Oh Sang, Sokół Janusz
Journal of Applied Analysis
|
2020
|
Vol. 26, nr 1
91--95
EN
In the class of analytic functions in the unit disc |z| < 1 we prove some new sufficient conditions for functions to be univalent or to be close-to-convex in the unit disc. Also we extend Ozaki’s condition that Re{exp(iα)f (p)(z)} > 0 in |z| < 1 implies that f(z) is at most p-valent in |z| < 1.
4
On the spectrum of an infinite-order differential operator and its relation to Hamiltonian mechanics
Akrami Seyed Ebrahim
Journal of Applied Analysis
|
2019
|
Vol. 25, nr 2
131--139
EN
We introduce an infinite-order linear differential operator and study its spectrum. We show that all analytical functions around the origin are its eigenfunctions corresponding to zero eigenvalue. We outline an interesting relation between this operator and the conservation law of energy in Hamiltonian mechanics.
5
Content available The real and complex convexity
Jamel A.
Journal of Mathematics and Applications
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2018
|
Vol. 41
123--156
EN
We prove that the holomorphic differential equation ϕ’’(ϕ+c) = γ(ϕ’)² (ϕ:C→C be a holomorphic function and (γ, c) ϵ C²) plays a classical role on many problems of real and complex convexity. The condition exactly γ ϵ [wzór] (independently of the constant c) is of great importance in this paper. On the other hand, let n ≥ 1, (A₁, A₂) ϵ C² and g₁, g₂ : Cᵑ → C be two analytic functions. Put u(z, w) = │A ₁w - g₁(z) │² + │A₂w - g₂(z) │²v(z,w) = │A₁w - g₁(z) │² + │ A₂w - g₂(z) │², for (z,w) ϵ Cᵑ x C. We prove that u is strictly plurisubharmonic and convex on Cᵑ x C if and only if n = 1, (A₁, A₂) ϵ C² \{0} and the functions g₁ and g₂ have a classical representation form described in the present paper. Now v is convex and strictly psh on Cᵑ x C if and only if (A₁, A₂) ϵ C² \{0}, n ϵ {1,2} and and g₁, g₂ have several representations investigated in this paper.
6
Content available remote Coefficient Estimate of bi-Bazilevič Functions Associated with Fractional q-calculus Operators
Murugusundaramoorthy G., Janani T., Purohit S. D.
Fundamenta Informaticae
|
2017
|
Vol. 151, nr 1/4
49--62
EN
In this paper, we introduce and investigate two new subclasses of the function class ∑ of bi-univalent functions defined in the open unit disk, which are associated with fractional q-calculus operators, satisfying subordinate conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients |a2| and |a3| for functions in these new subclasses. Several (known or new) consequences of the results are also pointed out.
7
Content available remote Cr-right equivalence of analytic functions
Migus P.
Demonstratio Mathematica
|
2015
|
Vol. 48, nr 2
313--321
EN
Let f, g : (Rn , 0) → (R, 0) be analytic functions. We will show that if (…) and (…) then f and g are Cr-right equivalent, where (f) denoteideal generated by f and (…).
8
Content available remote Fekete-Szego problem for certain subclasses of analytic functions
Orhan H., Deniz E., Caglar M.
Demonstratio Mathematica
|
2012
|
Vol. 45, nr 4
835-846
EN
In this present investigation, authors introduce certain subclasses of star like and convex functions of complex order b, using a linear multiplier differential operator (…). In this paper, for these classes the Fekete-Szegö problem is completely solved. Various new special cases of our results are also pointed out.
9
Content available remote Some general results and extreme points of p-valent functions with negative coefficients
Xiong L.
Demonstratio Mathematica
|
2011
|
Vol. 44, nr 2
261-272
EN
In this paper, we further investigate the class of functions (…) which are analytic in the open unit disk (…),and involve the combinations of the representations of p-valently starlike and convex functions. We obtain several generalized results on the modified-Hadamard product of the class (…) which extend the corresponding results obtained by Altintas et al. [Computers Math. Applic. 30(2), 9-16, (1995)]; Darwish, Aouf [Mathematical and Computer Modelling (2007), doi:10.1016/j.mcm.2007.08.016 ]. Futher, by fixing the second coefficient of functions in (…) we introduce the special class (…) and discuss the extreme points.
10
Content available remote A new class of multivalent analytic functions defined by the hadamard product
Dziok J.
Demonstratio Mathematica
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2011
|
Vol. 44, nr 2
233-251
EN
The object of the present paper is to investigate the coefficients estimates, distortion properties, the radii of starlikeness and convexity, subordination theorems, partial sums and integral mean inequalities for classes of functions with two fixed points. Some remarks depicting consequences of the main results are also mentioned.
11
Content available remote Generalized classes of uniformly convex functions
Dziok J., Szpila A.
Journal of Mathematics and Applications
|
2010
|
Vol. 33
13-26
EN
In this paper we introduce some subclasses of analytic functions with varying argument of coeffcients. These classes are defined in terms of the Hadamard product and generalize the well-known classes of uniformly convex functions. We investigate the coeffcients estimates, distortion properties, radii of starlikeness and convexity for defined classes of functions.
12
On univalent functions defined by a generalized differential operator
Ibrahim R. W., Darus M.
Journal of Applied Analysis
|
2010
|
Vol. 16, nr 2
305-313
EN
The object of this paper is to derive some inclusion relations regarding a new class by using the generalized differential operator due to the authors.
13
Content available remote Properties of certain classes of analytic functions defined by Srivastava-Attiya operator
Khairnar S., More M.
Demonstratio Mathematica
|
2010
|
Vol. 43, nr 1
55-79
EN
In this paper we introduce the class K(s,b,beta,apha) of analytic functions defined by the Srivastava-Attiya convolution operator Js,b(f) involving the Hurwitz-Lerch Zeta function. We derive few subordination results for the functions in the class K(s,b,beta,alpha) and discuss the interesting applications of subordination results with the help of convex functions. Several other properties like coefficient inequalities growth and distortion theorems, extreme points, integral mean inequalities, partial sums and quasi-Hadamard product are investigated for the class K(s,b,beta,alpha). The authors also obtain Fekete-Szego inequality for normalized analytic functions f(z) defined on the open unit disc for which [....] lies in a region starlike with respect to 1 and is symmetric with respect to the real axis. Applications of our main result involving the Owa-Srivastava operator of fractional calculus are discussed. Finally as one of the applications of our result, we derive the Fekete-Szego inequality for a class of normalized analytic functions, defined using the Hadamard product and the Owa-Srivastava operator.
14
Content available remote New sufficient conditions for starlikeness of analytic functions involving a fractional differintegral operator
Prajapat J. K., Raina R. K.
Demonstratio Mathematica
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2010
|
Vol. 43, nr 4
805-813
EN
In this paper we apply a fractional differintegral operator to a class of analytic functions and derive certain new sufficient conditions for the starlikeness of this class of functions. The usefulness of the main results are depicted by deducing several interesting corollaries and relevances with some of the earlier results are also pointed out.
15
Content available remote Certain class of p-valent functions associated with the wright generalized hypergeometric function
Aouf M., Shamandy A., Mostafa A., Madian S.
Demonstratio Mathematica
|
2010
|
Vol. 43, nr 1
39-54
EN
Using the Wright's generalized hypergeometric function, we introduce a new class Wk (p, q, s; A, B, lambda) of analytic p-valent functions with negative coefficients. In this paper we investigate coefficients estimates, distortion theorem, the radii of p-valent starlikeness and p-valent convexity and modified Hadamard products.
16
Sandwich theorems for certain subclasses of analytic functions defined by family of linear operators
Mostafa A. O., Aouf M. K.
Journal of Applied Analysis
|
2009
|
Vol. 15, nr 2
269-280
EN
In this paper, we obtain some applications of first order differential subordination and superordination results involving Dziok-Srivastava operator and other linear operators for certain normalized analytic functions in the open unit disk. The results, which are presented in this paper, have relevant connections with various previous results.
17
Content available remote On an application of certain sufficient condition for starlikeness
Sokół J.
Journal of Mathematics and Applications
|
2008
|
Vol. 30
131-135
EN
In this paper we consider a sufficient condition for furiction to be a-starlike function, when α ∈ [0, 1/2]. We use it for certain subclass of strongly starlike functions defined by a geometric condition. We take advantage of the techniąues of differential subordinations.
18
Content available remote Classes of functions defined by subordination
Dziok J., Stankiewicz J.
Journal of Mathematics and Applications
|
2008
|
Vol. 30
53-59
EN
In the paper, we define classes of analytic functions, in terms of subordination. We present some inclusion relations for defined classes.
19
Content available remote Certain subclass of multivalent functions involving the Cho-Kwon-Srivastava operator
Zeng T., Gao Ch-Y., Wang Z-G., Aghalary R.
Journal of Mathematics and Applications
|
2008
|
Vol. 30
161-170
EN
In the present paper, we introduce a new subclass S(sup (j)) (sub p, λ) (α; a, c; φ) of multivalent functions involving the Cho-Kwon-Srivastava operator. Such results as inclusion relationships, coefficient estimates and convolution properties for this class are proved. The results presented here would provide extensions of those given in earlier works.
20
Content available remote On certain class of analytic functions associated with a convolution structure
Murugusundaramoorthy G., Raina R.
Demonstratio Mathematica
|
2008
|
Vol. 41, nr 3
551-559
EN
Making use of a convolution structure, we introduce a new class of analytic functions defined in the open unit disc and investigate its various characteristics. Apart from deriving a set of coefficient bounds, we establish several inclusion relation-ships involving the (n, [...)-neighborhoods of analytic functions with negative coefficients belonging to this subclass.
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