Osman Altintas

Neighborhoods of a class of analytic functions with negative coefficients

Abstract By making use of the familiar concept of neighborhoods of analytic functions, the authors prove several inclusion relations associated with the (n, δ)-neighborhoods of various subclasses of starlike and convex functions of complex order. Special cases of some of these inclusion relations are shown to yield known results.

Neighborhoods of certain analytic functions with negative coefficients

The object of the present paper is to derive some properties of neighborhoods of analytic functions with negative coefficients in the open unit disk.

Majorization by starlike functions of complex order

The authors investigate several majorization problems involving starlike and convex functions 01 complex order as well as functions belonging to a certain class: R(λ,γ) which they introduce here Relevant connections of the main results obtained in those paper with those given by earlier workers on the subject are also pointed out

Fractional calculus and certain starlike functions with negative coefficients

Abstract A certain subclass T ( n , p , λ , α ) of starlike functions in the unit disk is introduced. The object of the present paper is to derive several interesting properties of functions belonging to the class T ( n , p , λ , α ). Various distortion inequalities for fractional calculus of functions in the class T ( n , p , λ , α ) are also given.

Coefficient bounds for some families of starlike and convex functions of complex order

Abstract In the present work, the authors determine coefficient bounds for functions in certain subclasses of starlike and convex functions of complex order, which are introduced here by means of a family of nonhomogeneous Cauchy–Euler differential equations. Several corollaries and consequences of the main results are also considered.

Neighborhoods for certain subclasses of multivalently analytic functions defined by using a differential operator

In the present investigation, by making use of the familiar concept of neighborhoods of analytic and multivalent functions, we derive coefficient bounds and distortion inequalities, associated inclusion relations for the (n,@d)-neighborhoods of subclasses of analytic and multivalent functions with negative coefficients, which are defined by means of a certain nonhomogenous differential equation. Several special cases of the main results are mentioned.

Neighborhoods of certain p-valently analytic functions with negative coefficients

In this investigation, by making use of the familiar concept of neighborhoods of p-valently analytic functions, the authors prove coefficient bounds, distortion inequalities, associated inclusion relations for the (n, δ)-neighborhoods of a family of p-valently analytic functions and its certain derivatives, which is defined by means of a certain non-homogenous differential equation.

Applications of differential subordination

In this work, the authors introduce several new subclasses of analytic functions in the unit disk and investigate various inclusion properties of these subclasses. Also, we determine inclusion relationships between these new subclasses and other known classes.

Coefficient bounds for certain subclasses of starlike functions of complex order

Abstract In this work, we determine the coefficient bounds for functions in certain subclasses of starlike and convex functions of complex order, which are introduced here by means of a certain non-homogeneous Cauchy–Euler-type differential equation of order m . Several corollaries and consequences of the main results are also considered.

A subclass of analytic functions defined by using certain operators of fractional calculus

Making use of certain operators of fractional calculus, we introduce a new class F6(n,A,a) of functions which are analytic in the open unit disk /4 and obtain a necessary and sufficient condition for a function to be in the class Fs(n,A, ct). We also determine the radii of close-to-convexity, starlikenees, and convexity. Finally, an application involving fractional calculus of functions in the class F6(n, A, a) is considered.