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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2022.4
- 수록면
- 455 - 472 (18page)
- DOI
- 10.4134/CKMS.c210072
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초록· 키워드
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For $j=0,1,2,\ldots,k-1;~~k\geq 2;~\text{and}~-1\leq B<A\leq1$, we have introduced the functions classes denoted by $\mathcal{ST}_{[j,k]}(A,B)$ and $\mathcal{K}_{[j,k]}(A,B)$, respectively, called the generalized $(j,k)$-symmetric starlike and convex functions. We first proved the sharp bounds on $| f(z)|$ and $| f^{\prime}(z)|$. Various radii related problems, such as radius of $(j,k)$-symmetric starlikeness, convexity, strongly starlikeness and parabolic starlikeness are determined. The quantity $| a_{3}^{2}-a_{5}|$, which provide the initial bound on Zalcman functional is obtained for the functions in the family $\mathcal{ST}_{[j,k]}.$ Furthermore, the sharp pre-Schwarzian norm is also established for the case when $f$ is a member of $\mathcal{K}_{[j,k]}(\alpha)$ for all $0\leq \alpha <1.$
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