Let 𝝨 be the class of meromorphic bi-univalent functions f of the formf(z)=z+b_0+∑ _(n=1)^∞ ▒ b_n/z^n, which are univalent (analytic and one to one) on the domain Δ ={z∈ C∶ 1.

In this paper, we introduce and investigate a subclass Hh, pS(b) of analytic and bi-univalent functions in the open unit disk U. Upper bounds for the second and third coefficients of functions in this subclass are founded. Our results generalize and improve over the existing results in the literature.

The purpose of the present paper is to introduce two new subclasses of the function class ∑m of bi-univalent functions which both f and f-1 are m-fold symmetric analytic functions. Furthermore, we obtain estimates on the initial coefficients for functions in each of these new subclasses. Also we explain the relation between our results with earlier known results.

In this study, performance records of the native Fars chickens collected by the Fars Native fowls Breeding Centers, during 1988 to 1999 were analyzed. The multi-trait animal model and restricted maximum likelihood procedure was used to estimate heritability, correlations between traits and breeding values. estimates of heritabilities were 0.68, OAO,0.64 and OA9 for body weight at 12 weeks (BW12), egg number (EN), egg weight (EW) and age of sexual maturity(ASM), respectively. The Cumulative genetic gains, after 8 generations of selection, expressed by regression coefficients of breeding values on generation for BW12, EN, EW and ASM, were 22.73,0.17,0.04 and -1.38, respectively. A pedigree file collected on 21245 female and male birds was used to calculate the inbreeding coefficient. The average inbreeding coefficients for all birds were 0.048%, and ranged from zero to 25%. In this population, 8% of the birds were inbred, and average inbreeding coefficients for inbred bird was 0.67% Due to relatively high heritability of productive and reproductive traits, it is possible to achieve more progress in these traits using appropriate genetic selection.

In this paper, we introduce and investigate a subclass  $\mathcal{G}_{\Sigma}^{h,p}(\lambda,m,n, \alpha,\gamma)$ of bi-univalent functions in the open unit disk $\mathbb{U}$. Upper bounds for this class's second and third coefficients of functions are found. The results, which we have presented in this paper, would generalize and improve some recent works of several earlier authors.

In the present paper, we introduce a new subclass H∑m (λ, β)of the m-fold symmetric bi-univalent functions. Also, we find the estimates of the Taylor-Maclaurin initial coefficients |am+1|, |a2m+1| and general coefficients |amk+1| (k ≥ 2) for functions in this new subclass. The results presented in this paper would generalize and improve some recent works of several earlier authors.

The purpose of the present paper is to introduce a class $\boldsymbol{D}% _{\lambda, \delta }^{k, \alpha }C_{0}(\beta )$ of bi-concave functions defined by a differential operator. We find estimates on the Taylor-Maclaurin coefficients $\left\vert a_{2}\right\vert $ and $\left\vert a_{3}\right\vert $ for functions in this class. Several consequences of these results are also pointed out in the form of corollaries.