Let D ⊂ C and 0 ∈ D. A set D is circularly symmetric if for each % ∈ R a set D ∩ {ζ ∈ C : |ζ| = %} is one of three forms: an empty set, a whole circle, a curve symmetric with respect to the real axis containing %. A function f ∈ A is circularly symmetric if f(∆) is a circularly symmetric set. The class of all such functions we denote by X. The above definitions were given by Jenkins in [2]. In ...

In this paper, we shall introduce the fuzzyw-distance, then prove a common fixed point theorem with respectto fuzzy w-distance for two mappings under the condition ofweakly compatible in complete fuzzy metric spaces.

In the past few years, many scholars gave much attention to use of q-calculus in geometric functions theory, and they defined new subclasses analytic harmonic functions. While using symmetric function very little work has been published so far. this research, with help fundamental concepts q-Salagean differential operator for functions, we define a class connected Janowski SH0˜m,q,A,B. First, i...

In the present article, using subordination principle, authors employed certain generalized multiplier transform to define two new subclasses of analytic functions with respect symmetric and conjugate points. particular, bi-univalent conditions for function f(z) belonging these their relevant connections famous Fekete-Szegö inequality |a3−va22| were investigated a succinct mathematical approach.

A new subclass R(u), 0 < u < I, of the class St(I/2) the class of starlike functions of order I/2 is introduced and it is shown that R(u) is closed with respect to the Hadamard product of analytic functions. Some sufficient conditions for the normalized regular functions to be univalent in the unit disk E are given.

Let $p$ be an analytic function defined on the open unit disc $mathbb{D}$ with $p(0)=1.$ The conditions on $alpha$ and $beta$ are derived for $p(z)$ to be subordinate to $1+4z/3+2z^{2}/3=:varphi_{C}(z)$ when $(1-alpha)p(z)+alpha p^{2}(z)+beta zp'(z)/p(z)$ is subordinate to $e^{z}$. Similar problems were investigated for $p(z)$ to lie in a region bounded by lemniscate of Bernoulli $|w^{2}-1|=1$ ...