It is well-known that the logarithmic coefficients play an important role in the development of the theory of univalent functions. If denotes the class of functions analytic and univalent in the open unit disk , then the logarithmic coefficients of the function are defined by . In the current paper, the bounds for the logarithmic coefficients for some well-known classes like for and were estimated. Further, conjectures for the logarithmic coefficients for functions belonging to these classes are stated. For example, it is forecasted that if the function...

The aim of the present paper is to introduce a new class $\mathcal{G}\left(\alpha ,\delta \right)$ of analytic functions in the open unit disk and to study some properties associated with strong starlikeness and close-to-convexity for the class $\mathcal{G}\left(\alpha ,\delta \right)$ . We also consider sharp bounds of logarithmic coefficients and Fekete-Szegö functionals belonging to the class $\mathcal{G}\left(\alpha ,\delta \right)$ . Moreover, we provide some topics related to the results reported here that are relevant to outcomes presented in earlier research.

In this paper, various coefficient bounds of functions in some classes which are defined by subordination are estimated. Some special consequences of the main results are also presented. Moreover, it is pointed out that the given bounds improve and generalize some of the pervious results.

Let