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COEFFICIENT INEQUALITIES FOR JANOWSKI STARLIKENESS

SUSHIL KUMAR|SUMIT NAGPAL|V. Ravichandran
장전수학회 (Jangjeon Mathematical Society)|2016.01|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제19권 제1호|pp. 83-100|DOI 10.17777/pjms.2016.19.1.009

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참고문헌

키워드

SubordinationJanowski starlike functionconvex functionmeromorphic functioncoecient inequalitygrowth and distortionrational function
주제분류수학

초록

For -1 ≤ B < A ≤ 1, let S*[A,B] and K[A,B] be the classes of analytic functions f defined in the open unit disk normalized by the conditions f(0) = f'(0) - 1 = 0 satisfying the subordination relations zf'(z)/f(z) ∠(1 + Az)/(1 + Bz) and 1 + zf''(z)=f'(z) ∠ (1 + Az)=(1 + Bz) respectively. The necessary and sufficient coefficient conditions are obtained for normalized analytic functions f of the form (z/f(z))μ= 1 +∞∑n=1 bnzn, μ> 0 to be in the class S*[A,B]. For such functions, growth, covering and distortion theorems are also proved. In addition, a sufficient coefficient condition is also obtained for such functions to be in the class K[A,B]. Applications of obtained results are also provided. Analogous results are proved for meromorphic rational functions defined in the punctured open unit disk.

Abstract

For -1 ≤ B < A ≤ 1, let S*[A,B] and K[A,B] be the classes of analytic functions f defined in the open unit disk normalized by the conditions f(0) = f'(0) - 1 = 0 satisfying the subordination relations zf'(z)/f(z) ∠(1 + Az)/(1 + Bz) and 1 + zf''(z)=f'(z) ∠ (1 + Az)=(1 + Bz) respectively. The necessary and sufficient coefficient conditions are obtained for normalized analytic functions f of the form (z/f(z))μ= 1 +∞∑n=1 bnzn, μ> 0 to be in the class S*[A,B]. For such functions, growth, covering and distortion theorems are also proved. In addition, a sufficient coefficient condition is also obtained for such functions to be in the class K[A,B]. Applications of obtained results are also provided. Analogous results are proved for meromorphic rational functions defined in the punctured open unit disk.

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관련 논문AI추천

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