In Geometric function theory, occasionally, attempts have been made to solve a particular problem for the Ma-Minda classes, $$\mathcal {S}^*(\psi )$$ and {C}(\psi of univalent starlike convex functions, respectively. Recently, popular radius generally known as Bohr’s phenomenon has studied in various settings; however, little is about Rogosinski radius. this article, fixed $$f\in \mathcal or ),...

In this article, we are interested in finding sufficient conditions on A , B L , and id="M2"> η which ensure the normalized Coulomb wave function to be Janowski starlike. Sufficient also obtained for id="M3"> g / z ∈ <mi...

The theory of geometric functions was first introduced by Bernard Riemann in 1851. In 1916, with the concept normalized function revealed Bieberbach, univalent has found application area. Assume f(z)=z+??, n?(anzn) converges for all complex numbers z |z|&lt;1 and f(z)is one-to-one on set such z. Convex starlike f(z) g(z) are discussed help subordination. analytic unit disc f(0)=f'(0)=1, g(0)=0,...

‎let $x$ be a real normed  space, then  $c(subseteq x)$  is  functionally  convex  (briefly, $f$-convex), if  $t(c)subseteq bbb r $ is  convex for all bounded linear transformations $tin b(x,r)$; and $k(subseteq x)$  is  functionally   closed (briefly, $f$-closed), if  $t(k)subseteq bbb r $ is  closed  for all bounded linear transformations $tin b(x,r)$. we improve the    krein-milman theorem  ...

Abstract. The aim of this paper is to obtain coefficient estimates, distortion theorems, convex linear combinations and radii of close-toconvexity, starlikeness and convexity for functions belonging to the subclass TSγ(f, g; α, β) of uniformly starlike and convex functions, we consider integral operators associated with functions in this class. Furthermore partial sums fn(z) of functions f(z) i...