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We derive some results for a new class of analytic functions defined by using Salagean operator. We give some properties of functions in this class and obtain numerous sharp results including for example, coefficient estimates, distortion theorem, radii of star-likeness, convexity, close-to-convexity, extreme points, integral means inequalities, and partial sums of functions belonging to this class. Finally, we give an application involving certain fractional calculus operators that are also considered.

We introduce certain new classesκ−VST(α,β)andκ−VUCV(α,β), which represent theκuniformly starlike functions of orderαand typeβwith varying arguments and theκuniformly convex functions of orderαand typeβwith varying arguments, respectively. Moreover, we give coefficients estimates, distortion theorems, and extreme points of these classes.

We introduce a class of multivalent -uniformly functions with varying arguments, give some properties of functions in this class, and obtain sharp results including coefficient estimates and distortion theorems. Finally, we give the extreme points for this class.