SUBCLASSES OF BI-SAKAGUCHI FUNCTIONS ASSOCIATED WITH Q−DIFFERENCE OPERATOR

Hemen Dutta, S O OLATUNJI, M A ADENIYI

Abstract


In this work, the authors introduce a subclass $\zeta\Sigma^{\lambda}_{q}(b,\phi)$ in the open unit disk which associated with $q$-difference operator and satisfy some subordination conditions. The estimates for $\left|a_{2} \right|$ and $\left|a_{3} \right|$ were obtained by making use of Taylor-Maclaurin series. Also, the Fekete-Szeg$\ddot{o}$ inequality for the new class of functions are derived. Our results serve as a new generalization in this direction and still pave way for researchers to study this class by means of the Chebyshev polynomials and Sigmoid functions.

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The Thai Journal of Mathematics organized and supported by The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART).

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|ISSN 1686-0209|