fa تخمین دقیق ضرایب لگاریتمی رده‌ای خاص از توابع تحلیلی جبر alg علمی پژوهشی بنیادی S فرض&shy; کنید ردۀ همۀ توابع تحلیلی و نرمال&shy; شده در قرص واحد باشد. برای هر تابع &nbsp;از خانواۀ &nbsp;ضرایب لگاریتمی &nbsp;به&shy; صورت زیر تعریف می&shy;شوند: <div style="text-align: center;"></div><br> هم&shy;چنین، زیرردۀ &nbsp;از &nbsp;را به&shy;صورت زیر تعریف می&shy;کنیم<br> <br> که در آن &quot; &quot; رابطۀ تبعیت است. هدف ما در این مقاله تخمین دقیق نامساویها شامل ضرایب لگاریتمی برای توابعی است که به ردۀ &nbsp; &nbsp;تعلق دارند.<br> &nbsp; <strong>Introduction</strong><br> Let&nbsp;&nbsp;be the open unit disc in the complex plane&nbsp;&nbsp;and&nbsp;&nbsp;be the class of all functions of&nbsp;&nbsp;which are analytic and normalized in&nbsp;&nbsp;The subclass of&nbsp;consisting of all univalent functions&nbsp;&nbsp;in&nbsp;&nbsp;is denoted by&nbsp;&nbsp;We say that a function&nbsp;&nbsp;is said to be starlike function if and only if for all We denote by&nbsp;&nbsp;the class of all satrlike functions in&nbsp;If&nbsp;&nbsp;and&nbsp;&nbsp;are two of the functions in&nbsp;&nbsp;then we say that&nbsp;&nbsp;is subordinate to&nbsp;&nbsp;written&nbsp;&nbsp;or&nbsp;&nbsp;if there exists a Schwartz function&nbsp;&nbsp;such that&nbsp;&nbsp;for all&nbsp;&nbsp;Furthermore, if the function&nbsp;&nbsp;is univalent in&nbsp;&nbsp;then we have the following equivalence: Also for&nbsp;and&nbsp;&nbsp;&nbsp;their Hadamard product (or convolution) is defined by&nbsp;The logarithmic coefficients&nbsp;&nbsp;&nbsp;of&nbsp;, denoted by&nbsp;, are defined by These coefficients play an important role for various estimates in the theory of univalent functions. For example, consider the Koebe function where&nbsp;&nbsp;It is easy to see that the above function&nbsp;&nbsp;has logarithmic coefficients&nbsp;where&nbsp;&nbsp;and&nbsp;&nbsp;Also for the function&nbsp;&nbsp;we have and&nbsp;the sharp estimates&nbsp;and&nbsp;hold. We remark that the Fekete-Szego theorem is used. For&nbsp;&nbsp;, the problem seems much harder and no significant upper bounds for&nbsp;&nbsp;when&nbsp;&nbsp;appear to be known. Moreover, the problem of finding the sharp upper bound for&nbsp;for&nbsp;&nbsp;is still open for&nbsp;. The sharp upper bounds for modulus of logarithmic coefficients are known for functions in very few subclasses of&nbsp;. For functions in the class&nbsp;&nbsp;it is easy to prove that&nbsp;&nbsp;for&nbsp;&nbsp;and the equality holds for the Koebe function. The celebrated de Branges&#39; inequalities (the former Milin conjecture) for univalent functions&nbsp;&nbsp;state that where&nbsp;&nbsp;&nbsp;with the equality if and only if De Branges used this inequality to prove the celebrated Bieberbach conjecture. Moreover, the de Branges&#39; inequalities have also been the source of many other interesting inequalities involving logarithmic coefficients of&nbsp;&nbsp;such as&nbsp;&nbsp;&nbsp; Let&nbsp;&nbsp;denote the class of functions&nbsp;&nbsp;and satisfying the following subordination relation where&nbsp;.<br> <strong>Material and methods</strong><br> In this paper, first we obtain a subordination relation for the class&nbsp;&nbsp;and by making use of this relation we give two sharp estimates for the logarithmic coefficients of the function&nbsp;<br> <strong>Results and discussion</strong><br> We obtain two sharp estimates for the logarithmic coefficients of the function&nbsp;<br> <strong>Conclusion</strong><br> The following conclusions were drawn from this research. <ul> <li>Logarithmic coefficients &nbsp;of the function&nbsp;&nbsp;are estimated.</li> </ul> <img alt="" height="2" src="file:///C:Users1AppDataLocalTempmsohtmlclip11clip_image001.gif" width="267" > تابع تک‌ارز, ستاره‌واری, تبعیت, ضرایب لگاریتمی, ضرب پیچشی Univalent functions, Starlikeness, Subordination, Logarithmic coefficients, Hadamard product. 441 448 http://mmr.khu.ac.ir/browse.php?a_code=A-10-552-1&slc_lang=fa&sid=1 Rahim Kargar رحیم کارگر rkargar1983@gmail.com 10031947532846004040 10031947532846004040 No سازمان مرکزی دانشگاه پیام نور، تهران Ali Ebadian علی عبادیان a.ebadian@urmia.ac.ir 10031947532846004041 10031947532846004041 No Department of mathematics, Faculty of Science, Urmia University, Urmia, Iran. دانشگاه ارومیه. دانشکده علوم. گروه ریاضی Nader Kanzi نادر کنزی n.kanzi@pnu.ac.ir 10031947532846004042 10031947532846004042 Yes سازمان مرکزی دانشگاه پیام نور، تهران