In the present investigation, we consider two new general subclasses $\mathcal {H}_{\Sigma }(\tau , \mu , \lambda , \gamma ; \alpha )$ and $\mathcal {H}_{\Sigma }(\tau , \mu , \lambda , \gamma ; \beta )$ of the class $\Sigma $ consisting of analytic and bi-univalent functions in the open unit disk $\mathbb {U}$. For functions belonging to the two classes introduced here, we find estimates on the Taylor–Maclaurin coeffcients $|a_{2}|$ and $|a_{3}|$. Several connections to some of the earlier known results are also pointed out.

Coefficient estimates for some general subclasses of analytic and bi-univalent functions

Abstract In this work, considering a general subclass of analytic bi-univalent functions, we determine estimates for the general Taylor–Maclaurin coefficients of the functions in this class. For this purpose, we use the Faber polynomial expansions. In certain cases, our estimates improve some of those existing coefficient bounds.

Faber polynomial coefficient estimates for a comprehensive subclass of analytic bi-univalent functions Estimations des coefficients polynômes de Faber pour une sous-classe complète de fonctions analytiques bi-univalentes

Faber polynomial coefficient estimates for a comprehensive subclass of analytic bi-univalent functions

In the present paper, a subclass of analytic and biunivalent functions by means of Gegenbauer polynomials is introduced. Certain coefficients bound for functions belonging to this subclass are obtained. Furthermore, the Fekete-Szego problem for this subclass is solved. A number of known or new results are shown to follow upon specializing the parameters involved in our main results.

/pdf/fekete-szego-inequality-for-analytic-and-bi-univalent-2grqrvzksi.pdf

Fekete-Szego Inequality for Analytic and Bi-univalent Functions Subordinate to Chebyshev Polynomials

The purpose of the present paper is to investigate some characterization for Poisson distribution series to be in the new subclasses $G(\lambda, \alpha)$ and $K(\lambda, \alpha)$  of analytic functions.

/pdf/some-inclusion-results-of-certain-subclass-of-analytic-1yelj0ru3x.pdf

Some inclusion results of certain subclass of analytic functions associated with Poisson distribution series

We introduce and investigate a new subclass of the function class of biunivalent functions of complex order defined in the open unit disk, which are associated with the Hohlov operator, satisfying subordinate conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients <path id="x1D44E" d="M483 97q-42 -50 -88.5 -79.5t-68.5 -29.5q-37 0 -17 93l22 102h-2q-54 -79 -144 -149q-59 -46 -100 -46q-24 0 -43 29t-19 86q0 78 34.5 153t94.5 120q41 31 94 51.5t98 20.5q29 0 72 -9q26 -6 39 -6l2 -4q-30 -117 -67 -323q-8 -41 2 -41q16 0 79 58zM374 387
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q0 45 -26.5 69.5t-68.5 24.5q-67 0 -120 -79l-20 20l43 63q51 56 127 56h1q66 0 107 -37t41 -95q0 -42 -31 -71q-22 -23 -68 -54z"> for functions in this new subclass. Several, known or new, consequences of the results are also pointed out.

/pdf/coefficient-estimate-of-biunivalent-functions-of-complex-2e7d33mnkx.pdf

Coefficient Estimate of Biunivalent Functions of Complex Order Associated with the Hohlov Operator

Coefficient estimates for certain classes of meromorphic bi-univalent functions

The purpose of the present paper is to investigate some characterization for generalized Bessel functions of first kind to be in the new subclasses of β uniformly starlike and β uniformly convex functions of order α. Further we point out consequences of our main results.

/pdf/an-application-of-generalized-bessel-functions-on-certain-3bqlg3y26e.pdf

An Application of Generalized Bessel Functions on Certain Subclasses of Analytic Functions

In the present investigation, we obtain initial coefficientsof �− pseudo starlike functions related to sigmoid functions and the Fekete-Szego coefficient functional|a3−µa 2 | for certain normalized analytic functions defined on the open unit disk. As an application of the main result,we pointed out the initial coefficients and Fekete-Szego inequality for a s ubclasses of starlike functions related to sigmoid functions.

/pdf/sigmoid-function-in-the-space-of-univalent-lambda-pseudo-2ddjvlidll.pdf

SIGMOID FUNCTION IN THE SPACE OF UNIVALENT $\lambda$-PSEUDO STARLIKE FUNCTIONS

We introduce a new class of meromorphic parabolic starlike functions with a fixed point defined in the punctured unit disk involving the -hypergeometric functions. We obtained coefficient inequalities, growth and distortion inequalities, and closure results for functions . We further established some results concerning convolution and the partial sums.

/pdf/meromorphic-parabolic-starlike-functions-associated-with-1oqopmx8zj.pdf

T. Janani

Papers

Coefficient Estimate of Biunivalent Functions of Complex Order Associated with the Hohlov Operator

Coefficient estimates for certain classes of meromorphic bi-univalent functions

An Application of Generalized Bessel Functions on Certain Subclasses of Analytic Functions

SIGMOID FUNCTION IN THE SPACE OF UNIVALENT $\lambda$-PSEUDO STARLIKE FUNCTIONS

Meromorphic Parabolic Starlike Functions Associated with -Hypergeometric Series