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Radii of Starlikeness and Convexity for Analytic Functions with Fixed Second Coefficient Satisfying Certain Coefficient Inequalities

V. Ravichandran|Sumit Nagpal|Rajni Mendiratta
경북대학교 자연과학대학 수학과|2015.06|Kyungpook Mathematical Journal|제55권 제2호|pp. 395-410

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참고문헌

키워드

starlike functionsconvex functionsuniformly convex functionsradius problemsparabolic starlike functionsfixed second coefficient
주제분류수학

초록

For functions f(z)=z+a2 z2+a3 z3+ · · · with |a2|=2b, b ≥ 0, sharp radii of starlikeness of order α (0 ≤ α<1), convexity of order α (0 ≤ α<1), parabolic starlikeness and uniform convexity are derived when |an| ≤ M/n2 or |an| ≤ M n2 (M>0). Radii constants in other instances are also obtained.

Abstract

For functions f(z)=z+a2 z2+a3 z3+ · · · with |a2|=2b, b ≥ 0, sharp radii of starlikeness of order α (0 ≤ α<1), convexity of order α (0 ≤ α<1), parabolic starlikeness and uniform convexity are derived when |an| ≤ M/n2 or |an| ≤ M n2 (M>0). Radii constants in other instances are also obtained.

참고문헌 (25)

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