in this paper we obtain coefficient characterization‎, ‎extreme points and‎ ‎distortion bounds for the classes of harmonic $p-$valent functions‎ ‎defined by certain modified operator‎. ‎some of our results improve‎ ‎and generalize previously known results‎.

We introduce and investigate classes of (p,q)-starlike harmonic univalent functions defined by subordination. first obtained a coefficient characterization these functions. give necessary sufficient convolution conditions, distortion bounds, compactness extreme points for the with negative coefficients.

In this paper we obtain coefficient characterization‎, ‎extreme points and‎ ‎distortion bounds for the classes of harmonic $p-$valent functions‎ ‎defined by certain modified operator‎. ‎Some of our results improve‎ ‎and generalize previously known results‎.

Department of Mathematics and Astronomy University of Lucknow, Lucknow 226007, India sharma [email protected] pathakmamta [email protected] Abstract In this paper, a necessary and sufficient condition for a function to be in the class Tμ(α, p,A,B) of p-valent analytic functions involving fractional calculus operator is obtained. Distortion bounds, subordination result, convolution results ...

In the present paper, we introduce and investigate an interesting subclass K λ s (h) of analytic and close-to-convex functions in the open unit disk U . For functions belonging to the class K λ s (h) , we derive several properties as the convolution, the coefficient bounds, the covering theorem, the inclusion relationships as well as distortion theorem. The various results presented here would ...

A sufficient coefficient of this class is determined. It is shown that this coefficient bound is also necessary for the classM –– H n, λ, α if fn z h –– gn∈ MH n, λ, α , where h z z− ∑∞ k 2|ak|z, gn z −1 n ∑∞ k 1|bk|z and n ∈ N0. Coefficient conditions, such as distortion bounds, convolution conditions, convex combination, extreme points, and neighborhood for the class M –– H n, λ, α , are obta...

In the present paper, we are defining a subclass of harmonic univalent functions with positive coefficients in unit disc U by using fractional calculus operator. Further we obtain distortion bounds, extreme points and radii of convexity for functions belonging to this class and discuss a class preserving integral operator. Here we also determine that the class studied in this paper is closed un...

Abstract In this paper, we establish certain new subclasses of meromorphic harmonic functions using the principles q -derivative operator. We obtain criteria sense preserving and univalency. also address other important aspects, such as distortion limits, preservation convolution, convexity limitations. Additionally, with help sufficiency criteria, estimate sharp bounds real parts ratios to the...

In this paper, our main focus is to define a new subfamily of q-analogue analytic functions associated with the q-cosine function. Furthermore, we investigate some useful results such as necessary and sufficient condition based on convolution idea, growth distortion bounds, closure theorem, convex combination, radii starlikeness, extreme point theorem partial sums for newly-defined class.