In this paper, we introduce a new derivative operator involving q -Al-Oboudi differential for meromorphic functions. By using operator, define subclass of functions and obtain the Fekete–Szegő inequalities.

We consider the problem of approximating a convex gure in the plane by a pair r R of homothetic that is similar and parallel rectangles with r C R We show the existence of such a pair where the sides of the outer rectangle are at most twice as long as the sides of the inner rectangle thereby solving a problem posed by P olya and Szeg o If the n vertices of a convex polygon C are given as a sort...

By using the q-derivative operator and Legendre polynomials, some new subclasses of q-starlike functions bi-univalent are introduced. Several coefficient estimates Fekete–Szegö-type inequalities for in each these obtained. The results derived this article shown to extend generalize those earlier works.

In this paper, we introduce and investigate new subclasses of bi-univalent functions with respect to the symmetric points in U=z?C:z<1 defined by Bernoulli polynomials. We obtain upper bounds for Taylor–Maclaurin coefficients a2,a3 Fekete–Szegö inequalities a3??a22 these subclasses.

We investigate large sieve inequalities such as 1 m m X j=1 log P e j C 2 Z 2 0 log e P e d ; where is convex and increasing, P is a polynomial or an exponential of a potential, and the constant C depends on the degree of P , and the distribution of the points 0 1 < 2 < < m 2 . The method allows greater generality and is in some ways simpler than earlier ones. We apply our results to estimate t...

Three subclasses of analytic and bi-univalent functions are introduced through the use q?Gegenbauer polynomials, which a generalization Gegenbauer polynomials. For falling within these subclasses, coefficient bounds a2 a3 as well Fekete–Szegö inequalities derived. Specializing parameters used in our main results leads to number new results.

Let p be a trigonometric polynomial, non-negative on the unit circle T. We say that a measure σ on T belongs to the polynomial Szeg˝ o class, if dσ(e iθ) = σ ′ ac (e iθ)dθ + dσ s (e iθ), σ s is singular, and 2π 0 p(e iθ) log σ ′ ac (e iθ) dθ > −∞ For the associated orthogonal polynomials {ϕ n }, we obtain pointwise asymp-totics inside the unit disc D. Then we show that these asymptotics hold in...

For the first time, we attempted to define two new sub-classes of bi-univalent functions in open unit disc complex order involving Mathieu-type series, associated with generalized telephone numbers. The initial coefficients these classes were obtained. Moreover, also determined Fekete–Szegö inequalities for function and several related corollaries.

Let H be the class of functions f(z) of the form f(z) = z + ∑∞ n=2 anz , which are analytic in the unit disk U = {z : |z| < 1}. In this paper, the authors introduce a subclass M (α, λ, ρ) of H and study its some properties. The subordination relationships, inclusion relationships, coefficient estimates, the integral operator and covering theorem are proven here for each of the function classes....

"We study the FeketeSzego problem on open unit ball of a complex Banach space. Namely, inequalities are proved for class spirallike mappings relative to an arbitrary strongly accretive operator, and some its subclasses. Next, we consider families non-linear resolvents holomorphically vanishing at origin. We solve Fekete- Szego over these families."