in this paper, we introduce and investigate a subclass of analytic and bi-univalent functions in the open unit disk. upper bounds for the second and third coefficients of functions in this subclass are founded. our results, which are presented in this paper, generalize and improve those in related works of several earlier authors.

The Koebe One Quarter Theorem states that the range of any Schlicht function contains centered disc radius 1/4 which is sharp due to value at −1. A natural question finding polynomials set sharpness for polynomials. In particular, it was asked in [7] whether Suffridge [15] are optimal. For degree 1 and 2 obviously true. It demonstrated [10] 3 not optimal a promising alternative family introduce...

Abstract We study problems similar to the Koebe Quarter Theorem for close-to-convex polynomials with all zeros of derivative in $${\mathbb {T}}:=\{z\in {\mathbb {C}}:|z|=1\}$$ T : = { z ? C | ...

We introduce and study (metrically) quarter-stratifiable spaces and then apply them to generalize Rudin and Kuratowski-Montgomery theorems about the Baire and Borel complexity of separately continuous functions. The starting point for writing this paper was the desire to improve the results of V.K. Maslyuchenko et al. [MMMS], [MS], [KM], [KMM] who generalized a classical theorem of W.Rudin [Ru]...

In this paper, we study the geometry of lightlike hypersurfaces of an indefinite trans-Sasakian manifold with a quarter-symmetric metric connection. The main result is a characterization theorem for such a lightlike hypersurface of an indefinite generalized Sasakian space form. Mathematics Subject Classification: 53C25, 53C40, 53C50