The Poincaré inequality and entire functions

On the Poincaré-Friedrichs inequality for piecewise H1 functions in anisotropic discontinuous Galerkin finite element methods

The purpose of this paper is to propose a proof for the PoincaréFriedrichs inequality for piecewise H1 functions on anisotropic meshes. By verifying suitable assumptions involved in the newly proposed proof, we show that the Poincaré-Friedrichs inequality for piecewise H1 functions holds independently of the aspect ratio which characterizes the shape-regular condition in finite element analysis...

Coupled systems of equations with entire and polynomial functions

We consider the coupled system$F(x,y)=G(x,y)=0$,where$$F(x, y)=bs 0 {m_1}   A_k(y)x^{m_1-k}mbox{ and } G(x, y)=bs 0 {m_2} B_k(y)x^{m_2-k}$$with entire functions $A_k(y), B_k(y)$.We    derive a priory estimates  for the sums of the rootsof the considered system andfor the counting function of  roots.

On the Integral Representations of Generalized Relative Type and Generalized Relative Weak Type of Entire Functions

In this paper we wish to establish the integral representations of generalized relative type and generalized relative weak type as introduced by Datta et al [9]. We also investigate their equivalence relation under some certain conditions.

Growth analysis of entire functions of two complex variables

In this paper, we introduce the idea of generalized relative order (respectively generalized relative lower order) of entire functions of two complex variables. Hence, we study some growth properties of entire functions of two complex variables on the basis of the definition of generalized relative order and generalized relative lower order of entire functions of two complex variables.

Entire Functions and Borel's Directions.