Recently, Haji Mohd and Darus  revived the study of coefficient problems for univalent functions associated with quasi-subordination. Inspired largely by this article, we provide coefficient estimates with k-th root transform for certain subclasses of 𝒮 defined by quasi-subordination.
In this paper, we obtain initial coefficient bounds for functions belong to a subclass of analytic bi-univalent functions related to pseudo-starlike functions by using the Chebyshev polynomials and also we find Fekete-Szegö inequalities for this class.
Making use of the Faber polynomial coefficient expansions to a class of meromorphic bi-univalent functions, we obtain the general coefficient estimates for such functions and study their initial coefficient bounds. The coefficient bounds presented here are new in their own kind.
In this short communication, the recent differential transform method is proposed to compute Laplace transforms in an innovative manner. Unlike the common method of finding Laplace transforms, the method is free of integration and hence is of computational interest. A number of illustrative examples are given to show the efficiency and simplicity of the new technique.
In the present investigation, we obtain some subordination and superordination results involving Hadamard products for certain normalized analytic functions in the open unit disk. Relevant connections of the results, which are presented in this paper, with various other known results are also pointed out.
Financed by the National Centre for Research and Development under grant No. SP/I/1/77065/10 by the strategic scientific research and experimental development program:
SYNAT - “Interdisciplinary System for Interactive Scientific and Scientific-Technical Information”.