en عمومى General پژوهشي Research paper In the present paper, we introduce the class &Beta;_&theta;(&alpha;,&beta;) consisting of functions f, analytic in the unit disc ∆, normalized by the condition f(0)=0=f&#39;(0)-1 and satisfying the following two-sided inequality<br> &alpha;< Re{f&#39;(z)+(1+e^i&theta;)/2 zf&#39;&#39;(z)}<&beta;&nbsp; &nbsp; &nbsp;(z&isin;∆),<br> where &theta;∊(-&pi;,&pi;], 0<&alpha;<1 and &beta;>1. Integral representation, differential subordination results, coefficient estimates and Fekete-Szeg&ouml; coefficient functional associated with the k-th (k&ge;1) root transform [f(z^k)]^1/k for functions in the class&nbsp;&Beta;_&theta;(&alpha;,&beta;), are determined.<betaquad<br></betaquad<br> Univalent, Close-to-convex, Differential subordination, Coefficient estimates, Fekete-Szegö problem. 199 210 http://ijmsi.ir/browse.php?a_code=A-10-4830-1&slc_lang=en&sid=1 Hesam Mahzoon hesammahzoon1@gmail.com 100319475328460010234 100319475328460010234 Yes Department of Mathematics, Islamic Azad University, West Tehran Branch, Tehran, Iran Janusz Sokól jsokol@ur.edu.pl 100319475328460010235 100319475328460010235 No Faculty of Mathematics and Natural Sciences with College of Natural Sciences, University of Rzeszów, ul. Prof. Pigonia 1, 35-310 Rzesz´ow, Poland