Motivated by Carlson-Shaffer linear operator, we define here a new generalized linear operator. Using this operator, we define a class of analytic functions in the unit disk U. For this class, a majorization problem of analytic functions is discussed.

The object of the present paper is to derive some properties of analytic functions defined by the Carlson Shaffer linear operator L(a, c)f(z) .

Using the operator L(a, c) defined by Carlson and Shaffer, we a new subclass of analytic functions ML(λ, a, c). The well known Fekete-Szegö problem, upper bound Hankel determinant order two, coefficient fourth is determined. Our investigation generalises some previous results obtained in different articles.

In this paper, we derive several interesting subordination results for certain class of analytic functions defined by the linear operator L(a, c)f(z) which introduced and studied by Carlson and Shaffer [2].

In this paper, we study the new subclasses of analytic functions in the unit disk E by using Carlson Shaffer operator and generalized Janowski functions. These new analytic classes relates with the concept of functions of bounded radius rotation and bounded Mocanu variation. Inclusion results and convolution invariant property are investigated.

The main goal of this investigation is to obtain sharp upper bounds for Fekete-Szegö functional and the third Hankel determinant a certain subclass SL?u,v,? holomorphic functions defined by Carlson-Shaffer operator in unit disk. Finally, some special values parameters, several corollaries were presented.

This paper deals with a new subclass of univalent function associated the right half lemniscate Bernoulli. We have find upper bound Hankel determinant H3(1) for this by applying Carlson–Shaffer operator to it. The present work also certain properties newly defined subclass, such as order 3, co-efficient estimate, etc.

Keywords: Operator Hadamard product Bazilevic functions Starlike functions Hypergeometric functions p-valent functions a b s t r a c t Let AðpÞ; p 2 N, be a class of functions f : f ðzÞ ¼ z p þ P 1 k¼pþn a k z k analytic in the open unit disc E. We use Carlson–Shaffer operator for p-valent functions to define and study certain classes of analytic functions. Inclusion results, a radius problem a...

Abstract The main objective of this paper is to obtain necessary and sufficient condition for a subclass of uniformly convex functions and corresponding subclass of starlike functions with fixed second coefficient defined by Carlson and Shaffer operator for the function f(z) in UCT (α, β). Furthermore, we obtain extreme points, distortion bounds and closure properties for f(z) in UCT (α, β) by ...