Nihat Yağmur

Bio: Nihat Yağmur is an academic researcher from Erzincan University. The author has contributed to research in topics: Struve function & Convexity. The author has an hindex of 11, co-authored 25 publications receiving 520 citations.

Coefficient estimates for a general subclass of analytic and bi-univalent functions

Abstract: In this paper, we introduce and investigate an interesting subclass NΣh,p (λ, μ) of analytic and bi-univalent functions in the open unit disk U. For functions belonging to the class NΣh,p (λ, μ), we obtain estimates on the first two Taylor-Maclaurin coefficients |a2| and |a3|. The results presented in this paper would generalize and improve some recent works of Caǧlar et al. [3], Xu et al. [10], and other authors.

Coefficient bounds for new subclasses of bi-univalent functions

Abstract: In the present investigation, we consider two new subclasses N Σ (; ) and N Σ ( ; ) of bi- univalent functions defined in the open unit disk U = {z : |z| < 1}: Besides, we find upper bounds for the second and third coefficients for functions in these new subclasses.

Geometric Properties of Generalized Struve Functions

Abstract: In the present work our object is to establish some geometric properties (like univalence, starlikeness, convexity and close-to-convexity) for the generalized Struve functions. In order to prove our main results, we use the technique of differential subordinations developed by Miller and Mocanu, some inequalities, and some classical results of Ozaki and Fejer.

Starlikeness and Convexity of Generalized Struve Functions

Abstract: We give sufficient conditions for the parameters of the normalized form of the generalized Struve functions to be convex and starlike in the open unit disk.

Radii of starlikeness of some special functions

Abstract: Geometric properties of the classical Lommel and Struve functions, both of the first kind, are studied. For each of them, there different normalizations are applied in such a way that the resulting functions are analytic in the unit disc of the complex plane. For each of the six functions we determine the radius of starlikeness precisely.

Computation of Special Functions

Abstract: : Documentation is given for some subroutines which compute potentials and other functions. A set of subroutines uses rational approximations to compute Bessel functions of integral order. One subroutine uses the Debye approximation for the efficient computation of Bessel functions of complex argument and complex order. Empirical formulae have been developed to express the limiting boundaries of the modes of computation. (Author)

Coefficient Bounds for a Certain Class of Analytic and Bi-Univalent Functions

Abstract: In this paper, we introduce and investigate a subclass of analytic and bi-univalent functions in the open unit disk $\mathbb{U}$ . By using the Faber polynomial expansions, we obtain upper bounds for the coefficients of functions belonging to this analytic and bi-univalent function class. Some interesting recent developments involving other subclasses of analytic and bi-univalent functions are also briefly mentioned.

Initial coefficient bounds for a subclass of m-fold symmetric bi-univalent functions

Abstract: Let $\Sigma$ denote the class of functions $$f(z)=z+\sum_{n=2}^{\infty}a_nz^n$$ belonging to the normalized analytic function class $\mathcal{A}$ in the open unit disk $\mathbb{U}$, which are bi-univalent in $\mathbb{U}$, that is, both the function $f$ and its inverse $f^{-1}$ are univalent in $\mathbb{U}$. The usual method for computation of the coefficients of the inverse function $f^{-1}(z)$ by means of the relation $f^{-1}\big(f(z)\big)=z$ is too difficult to apply in the case of $m$-fold symmetric analytic functions in $\mathbb{U}$. Here, in our present investigation, we aim at overcoming this difficulty by using a general formula to compute the coefficients of $f^{-1}(z)$ in conjunction with the residue calculus. As an application, we introduce two new subclasses of the bi-univalent function class $\Sigma$ in which both $f(z)$ and $f^{-1}(z)$ are $m$-fold symmetric analytic functions with their derivatives in the class $\mathcal{P}$ of analytic functions with positive real part in $\mathbb{U}$. For functions in each of the subclasses introduced in this paper, we obtain the coefficient bounds for $|a_{m+1}|$ and $|a_{2m+1}|$.