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MSC 2010: 30C45

The main object of the present paper is to extend the univalence condition for a family of integral operators. Relevant connections of some of the results obtained in this paper with those in earlier works are also provided.

The main object of the present paper is to extend the univalence condition for a family of integral operators. Relevant connections of some of the results obtained in this paper with those in earlier works are also provided.

The authors obtain the Fekete-Szegő inequality (according to parameters $s$ and $t$ in the region $s^2+st+t^2<3$, $s\ne t$ and $s+t\ne 2$, or in the region $s^2+st+t^2>3,$ $s\ne t$ and $s+t\ne 2$) for certain normalized analytic functions $f\left(z\right)$ belonging to $k{\text{-UST}}_{\lambda ,\mu }^n(s,t,\gamma )$ which satisfy the condition $$\Re \left\{\frac{(s-t)z{\left(D_{\lambda ,\mu }^{n}f\left(z\right)\right)}^{\text{'}}}{D_{\lambda ,\mu }^{n}f\left(sz\right)-D_{\lambda ,\mu }^{n}f\left(tz\right)}\right\}>k\left|\frac{(s-t)z{\left(D_{\lambda ,\mu }^{n}f\left(z\right)\right)}^{\text{'}}}{D_{\lambda ,\mu }^{n}f\left(sz\right)-D_{\lambda ,\mu }^{n}f\left(tz\right)}-1\right|+\gamma ,z\in 𝒰.$$ Also certain applications of the main result a class of functions defined by the Hadamard product (or convolution) are given. As a special case of this result, the Fekete-Szegő inequality for a class of functions defined through fractional derivatives is obtained....

By making use of the known concept of neighborhoods of analytic functions we prove several inclusions associated with the $(j,\delta )$-neighborhoods of various subclasses of starlike and convex functions of complex order $b$ which are defined by the generalized Ruscheweyh derivative operator. Further, partial sums and integral means inequalities for these function classes are studied. Relevant connections with some other recent investigations are also pointed out.

In the present investigation we solve Fekete-Szegö problem for the generalized linear differential operator. In particular, our theorems contain corresponding results for various subclasses of strongly starlike and strongly convex functions

In the present investigation we solve Fekete-Szegö problem for the generalized linear differential operator. In particular, our theorems contain corresponding results for various subclasses of strongly starlike and strongly convex functions. In the present investigation we solve Fekete-Szegö problem for the generalized linear differential operator. In particular, our theorems contain corresponding results for various subclasses of strongly starlike and strongly convex functions.