Entire functions sharing a linear polynomial with linear differential polynomials

In the paper we study the uniqueness of entire functions sharing a linear polynomial with linear differential polynomials generated by them. The results of the paper improves the corresponding results of P. Li (Kodai Math J. 22: 446-457, 1999), Lahiri-Present author(G. K. Ghosh) (Analysis (Munich)31: 331-340,2011) and Lahiri-Mukherjee(Bull. Aust. Math. Soc. 85: 295-306, 2012).

Coefficients bounds in some subclass of analytic functions

In this paper we consider a class of analytic functions introduced by Mishra and Gochhayat, {\it Fekete-Szeg\"o problem for a class defined by an integral operator}, Kodai Math. J., 33(2010) 310--328, which is connected with $k$-starlike functions through Noor operator. We find inclusion relations and coefficients bounds in this class.

REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS WITH GENERALIZED TANAKA–WEBSTER 𝔇⊥-PARALLEL SHAPE OPERATOR

In a paper due to [I. Jeong, H. Lee and Y. J. Suh, Real hypersurfaces in complex two-plane Grassmannians with generalized Tanaka–Webster parallel shape operator, Kodai Math. J.34 (2011) 352–366] we have shown that there does not exist a hypersurface in G2(ℂm+2) with parallel shape operator in the generalized Tanaka–Webster connection (see [N. Tanaka, On non-degenerate real hypersurfaces, graded Lie algebras and Cartan connections, Japan J. Math.20 (1976) 131–190; S. Tanno, Variational problems on contact Riemannian manifolds, Trans. Amer. Math. Soc.314(1) (1989) 349–379]). In this paper, we introduce a new notion of generalized Tanaka–Webster 𝔇⊥-parallel for a hypersurface M in G2(ℂm+2), and give a characterization for a tube around a totally geodesic ℍ Pn in G2(ℂm+2) where m = 2n.