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.

A new basis {irk(z)}t.o for discrete analytic polynomials is presented for which the series 2k-o ak7Tk(z) converges absolutely to a discrete analytic function in the upper right quarter lattice whenever lim | ak \" k = 0. Introduction Let Z be the group of integers and consider functions / : Z X Z ^ C such that (1.1) f(x, y) + if(x + 1, y) / (* + 1, y + 1) if(x, y + 1) = 0 for every (x, y ) £ Z...

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.

We study integration in a class of Hilbert spaces of analytic functions defined on the Rs. The functions are characterized by the property that their Hermite coefficients decay exponentially fast. We use Gauss-Hermite integration rules and show that the errors of our algorithms decay exponentially fast. Furthermore, we study tractability in terms of s and log ε−1 and give necessary and sufficie...

We study formal and non-formal deformation quantizations of a family manifolds that can be obtained by phase space reduction from $\mathbb{C}^{1+n}$ with the Wick star product in arbitrary signature. Two special cases such are complex projective $\mathbb{CP}^n$ hyperbolic disc $\mathbb{D}^n$. generalize several older results to this setting: The construction products their explicit description ...

Abstract. It was shown by P. J. Davis that the Newton-Cotes quadrature formula is convergent if the integrand is an analytic function that is regular in a sufficiently large region of the complex plane containing the interval of integration. In the present paper, a bound on the error of the Newton-Cotes quadrature formula for analytic functions is derived. Also the bounds on the Legendre polyno...

in this paper, we study the convexity of the integral operator

in this article, by using chebyshev’s polynomials and chebyshev’s expansion, we obtain the best uniform polynomial approximation out of p2n to a class of rational functions of the form (ax2+c)-1 on any non symmetric interval [d,e]. using the obtained approximation, we provide the best uniform polynomial approximation to a class of rational functions of the form (ax2+bx+c)-1 for both cases b2-4a...

Fourier spectral method can achieve exponential accuracy both on the approximation level and for sQIving partial differential equations if the solutions are analytic. For a linear PDE with discontinuous solutions, Fourier spectral method will produce poor point-wise accuracy without post-processing, but still maintains exponential accuracy for all moments against analytic functions. In this not...