Using the Lebedev–Milin inequalities, bounds on logarithmic coefficients of an analytic function can be transferred to estimates itself and related functions. From this fact, study logarithmic-related problems a certain subclass univalent functions has attracted much attention in recent years. In our present investigation, starlike Se* connected with exponential mapping was considered. The main...

"A normalized function $f$ on the open unit disc is starlike (or convex) univalent if associated $zf'(z)/f(z)$ $1+zf''(z)/f'(z)$) a with positive real part. The radius of starlikeness or convexity usually obtained by using estimates for functions Using subordination, we examine various starlikeness, in particular, radii Janowski and order $\beta$, when either convex $(zf'(z)+\alpha z^2f''(z))/f...

Using the Al-Oboudi type operator, we present and investigate two special families of bi-univalent functions connected with activation function \(% \phi (s)=\ 2/(1+e^{-s}),\,s\in \mathbb{R}\) \(k\)-Fibonacci numbers. We derive bounds on initial coefficients Fekete-Szego functional for \(g_{\phi }(z)=z+\sum \limits_{j=2}^{\infty }\phi (s)d_{j}z^{j}\) in these introduced families. Furthermore, in...

The class S of functions g(z) = z + c 2 z 2 + c 3 z 3 + ... analytic and univalent in the unit disk Izr < 1 has been thoroughly studied, and its properties are well known. Our purpose is to investigate another class of functions which, by contrast, seems to have been rather neglected. This is the class S o of functions f ( z ) = 1 + a 1 z + a 2 z Z + . . , analytic, univalent, and nonvanishing ...

In this paper, we obtain some subordination results for certian subclasses of univalent functions defined by convolution.

Two classes of univalent harmonic functions on unit disc satisfying the conditions ∑∞ n=2(n−α)(|an|+|bn|) ≤ (1−α)(1−|b1|) and ∑∞ n=2 n(n−α)(|an|+|bn|) ≤ (1−α)(1−|b1|) are given. That the ranges of the functions belonging to these two classes are starlike and convex, respectively. Sharp coefficient relations and distortion theorems are given for these functions. Furthermore results concerning th...