In this research, we estimate the coefficient in class of Bazilevic functions ℬ1(α) related to Lemniscate Bernoulli on unit disk

Keywords: Operator Hadamard product Bazilevic functions Starlike functions Hypergeometric functions p-valent functions a b s t r a c t Let AðpÞ; p 2 N, be a class of functions f : f ðzÞ ¼ z p þ P 1 k¼pþn a k z k analytic in the open unit disc E. We use Carlson–Shaffer operator for p-valent functions to define and study certain classes of analytic functions. Inclusion results, a radius problem a...

For a certain subclass of Bazilevic functions, Faber polynomials expansions are used to obtain bi-univalent properties. Estimates on the $n$th Taylor-Maclaurin coefficients functions in this class found. Moreover, some special cases also indicated.

In the present article, we define a new family for holomorphic functions (so-called Bazilevic-Sakaguchi type functions) and determinate strong differential subordination superordination results these by investigating certain suitable classes of admissible functions. These are applied to obtain sandwich results.

Using $ (p, q) $-Lucas polynomials and bi-Bazilevic type functions of order $\rho +i\xi,$ we defined a new subclass biunivalent functions. We obtained coefficient inequalities for belonging to the subclass. In addition these results, upper bound Fekete-Szegö functional was obtained. Finally, some special values parameters, several corollaries were presented.