We study the size of the range of the derivatives of a smooth function between Banach spaces. We establish conditions on a pair of Banach spaces X and Y to ensure the existence of a C smooth (Fréchet smooth or a continuous Gâteaux smooth) function f from X onto Y such that f vanishes outside a bounded set and all the derivatives of f are surjections. In particular we deduce the following result...

The edge clique graph of a graph G is one having as vertices the edges of G, two vertices being adjacent if the corresponding edges of G belong to a common clique. We describe characterizations relative to edge clique graphs and some classes of chordal graphs, such as starlike, starlike-threshold, split and threshold graphs. In particular, a known necessary condition for a graph to be an edge c...

In this paper, we introduce a new class of analytic functions defined by a new convolution operator La (α, β). The new class of analytic functions Σ a,t α,β (ρ; h) in U ∗ = {z : 0 < |z| < 1} is defined by means of a hypergeometric function with an integral operator associated with the Hurwitz-Lerch Zeta function and differential subordination. The authors also introduces and investigates variou...

In recent years, the Hankel determinant bounds for different subclasses of analytic, starlike and symmetric functions have been discussed studied by many well-known authors. this paper, we first consider a new subclass analytic function then derive fourth bound class.

In this paper, we introduce some classes of univalent harmonic functions with respect to the symmetric conjugate points by means subordination, analytic parts which are reciprocal starlike (or convex) functions. Further, combining graph function, discuss bound Bloch constant and norm pre-Schwarzian derivative for classes.

In terms of Wright generalized hypergeometric function we define a class of analytic functions. The class generalize well known classes of k-starlike functions and k-uniformly convex functions. Necessary and sufficient coefficient bounds are given for functions in this class. Further distortion bounds, extreme points and results on partial sums are investigated.

This is an introductory survey on applications of the Julia variation to problems in geometric function theory. A short exposition is given which develops a method for treating extremal problems over classes F of analytic functions on the unit disk D for which appropriate subsets Fn can be constructed so that (i) F = ⋃ n Fn and (ii) for each f ∈ Fn a geometric constraint will hold that ∂f(D) wi...

This study introduces a subclass Sqs* of starlike functions associated with the q-analogue sine function defined in symmetric unit disk. article comprises investigation sharp coefficient bounds, and upper bound third-order Hankel determinant for this class. It also includes findings Zalcman generalized conjectures

Analytic functions are characterized by the geometry of their image domains. That?s why, domain is substantial importance to have a comprehensive study analytic functions. To introduce and new geometrical structures as define subsequent an ongoing part research in geometric function theory. We introduced named cardioid defined corresponding function, see [14]. Here we further domain, starlike a...

Some new positive trigonometric sums that sharpen Vietoris’s classical inequalities are presented. These sharp inequalities have remarkable applications in geometric function theory. In particular, we obtain information for the partial sums of certain analytic functions that correspond to starlike functions in the unit disk. We also survey some earlier results with additional remarks and comments.