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The aim of this work is to introduce two families, $ \mathcal{B}_{\Sigma}(\wp; \vartheta) $ and $ \mathcal{O}_{\Sigma}(\varkappa; \vartheta) $, of holomorphic and bi-univalent functions involving the Bazilevič functions and the Ozaki-close-to-convex functions, by using generalized telephone numbers. We determinate upper bounds on the Fekete-Szegö type inequalities and the initial Taylor-Maclaurin coefficients for functions in these families. We also highlight certain edge cases and implications for our findings.

The purpose of this present paper is to investigate some mapping properties of functions which map the unit disc onto a overlapped leaf-like curve, having real part greater than zero. Also we define a class of λ-pseudo starlike functions related to a leaf-like curve. Integral representation, inequalities for the initial Taylor-Maclaurin coefficients and Fekete-Szegö problem for subclasses of analytic functions related to various conic regions are obtained as our main results.

In the article we introduce and investigate several new subclasses of q-starlike and q-convex type analytic and multivalent functions involving a generalized Bernardi integral operator, and establish the Fekete-Szegö type functional inequalities for these function classes. Besides, the corresponding bound estimates of the coefficients ap+1 and ap+2 are obtained.

The purpose of this paper is to introduce and study a new subclass of analytic functions with respect to symmetric points associated to a conic region impacted by Janowski functions. Also, the study has been extended to quantum calculus by replacing the ordinary derivative with a q-derivative in the defined function class. Interesting results such as initial coefficients of inverse functions and Fekete-Szegö inequalities are obtained for the defined function classes. Several applications, known or new of the main results are also presented.

Using the (p, q)-derivative operator we introduce new subclasses of analytic and bi-univalent functions, we obtain estimates on coefficients and the Fekete-Szegö functional.

Quasi-subordination which is an extension of the majorization and subordination principle, has been used to define a subclass of Bazilevič functions of complex order. Various classes of analytic functions that map unit disc onto conic domains and some classes of special functions are studied in dual. Inequalities for the initial Taylor-Maclaurin coefficients and unified solution of Fekete-Szegö problem for subclasses of analytic functions related to various conic regions are our main results. Our main results have many applications which are presented in the form of corollaries.

In the article we introduce several new subclasses of analytic functions associated with pedal shaped functions. By using differential subordination and convolution operator theory, we obtain the bound estimations of the coefficients a2 and a3, and the logarithmic coefficients d1 and d2 as well as Fekete-Szegö type functional inequalities for these subclasses.

In this paper, making use of the q-analogue of Carlson-Shaffer operator Lq(a,c) we introduce a new subclass of spiral-like functions and discuss some subordination results and Fekete-Szego problem for this generalized function class. Further, some known and new results which follow as special cases of our results are also mentioned.