Some properties for certain class of analytic functions defined by convolution

In this paper, we introduce a new class H_{T}(f,g;\alpha ,k) of analytic functions in the open unit disc U={z\in \mathbb{C}: left\vert z \right\vert <1} defined by convolution. The object of the present paper is to determine coefficient estimates, extreme points, distortion theorems, partial sums and integral means for functions belonging to the class H_{T}(f,g;\alpha ,k). We also obtain several results for the neighborhood of functions belonging to this class

A new generalization of the Takagi function

We consider a one-parameter family of functions $\{F(t,x)\}_{t}$ on $[0,1]$ and partial derivatives $\partial_{t}^{k} F(t, x)$ with respect to the parameter $t$. Each function of the class is defined by a certain pair of two square matrices of order two. The class includes the Lebesgue singular functions and other singular functions. Our approach to the Takagi function is similar to Hata and Yamaguti. The class of partial derivatives $\partial_{t}^{k} F(t, x)$ includes the original Takagi function and some generalizations. We consider real-analytic properties of $\partial_{t}^{k} F(t, x)$ as a function of $x$, specifically, differentiability, the Hausdorff dimension of the graph, the asymptotic around dyadic rationals, variation, a question of local monotonicity and a modulus of continuity. Our results are extensions of some results for the original Takagi function and some generalizations.Comment: 22 pages, 2 figures. The structure of paper has been changed significantl

On certain subclasses of meromorphic functions associated with certain integral operators

AbstractLet Σ denote the class of functions of the form f(z)=1z+∑k=1∞akzk which are analytic in 0<|z|<1. Two new integral operators Pβα and Qβα defined on Σ are introduced. This paper gives some subordination and convolution properties of certain subclasses of meromorphic functions which are defined by the previously-mentioned integral operators

Convolution properties for certain classes of multivalent functions

AbstractRecently N.E. Cho, O.S. Kwon and H.M. Srivastava [Nak Eun Cho, Oh Sang Kwon, H.M. Srivastava, Inclusion relationships and argument properties for certain subclasses of multivalent functions associated with a family of linear operators, J. Math. Anal. Appl. 292 (2004) 470–483] have introduced the class Sa,cλ(η;p;h) of multivalent analytic functions and have given a number of results. This class has been defined by means of a special linear operator associated with the Gaussian hypergeometric function. In this paper we have extended some of the previous results and have given other properties of this class. We have made use of differential subordinations and properties of convolution in geometric function theory

On Some Analytic Functions Defined by a Multiplier Transformation

We introduce and study a new class of analytic functions defined in the unit disc using a certain multiplier transformation. Some inclusion results and other interesting properties of this class are investigated

Study of the fuzzy q−spiral-like functions associated with the generalized linear operator

Nowadays, the subclasses of analytic functions in terms of fuzzy subsets are studied by various scholars and some of these concepts are extended using the $q-$theory of functions. In this inspiration, we introduce certain subclasses of analytic function by using the notion of fuzzy subsets along with the idea of $q-$calculus. We present the $q-$extensions of the fuzzy spiral-like functions of a complex order. We generalize this class using the $q-$analogues of the Ruscheweyh derivative and Srivastava-Attiya operators. Various interesting properties are examined for the newly defined subclasses. Also, some previously investigated results are deduced as the corollaries of our major results