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A Class of Multivalent Functions with Negative Coefficients Defined by Convolution

V. Ravichandran|R. M. Ali|M. H. Khan|K. G. Subramanian
대한수학회 (The Korean Mathematical Society)|2006.02|대한수학회보 (Bulletin of the KMS)|제43권 제1호|pp. 179-188

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Abstract

For a given $p$-valent analytic function $g$ with positive coefficients in the open unit disk $\UD$, we study a class of functions $f(z)=z^p-\sum_{n=m}^\infty a_nz^n$\ ($a_n\geq 0$) satisfying \[ \frac{1}{p}\Re \left( \frac{z(f*g)'(z)}{(f*g)(z)}\right) > \alpha\quad (0\leq \alpha<1; z\in\Delta).\] Coefficient inequalities, distortion and covering theorems, as well as closure theorems are determined. The results obtained extend several known results as special cases.

참고문헌 (5)

  1. "Hadamard products of analytic functions definedby Ruscheweyh derivatives", pp.13~ (1992), WorldSci. Publishing
  2. "On starlike functions with negativecoefficients", 8(3), pp.359~364 (2003)
  3. "Subclasses of univalent functions Lecture Notes in Mathematics 1013", pp.362~, in Complex analysis fifthRomanian-Finnish seminar Springer-Verlag
  4. "Univalent functions with negativecoefficients", 51, pp.109~ (1975)
  5. "Univalent functions with negativecoefficients", 51, pp.109~ (1975)

관련 논문AI추천

On a subclass of certain starlike functions with negative coefficientsHalit Orhan, Muhammet Kamali대한수학회 · 대한수학회보2004 · 제41권 제1호The Quasi-Hadamard Products of Certain $p$-Valent Functions With Negative CoefficientsMohamed Kamal Aouf대한수학회 · 대한수학회보2007 · 제44권 제4호On a Class of Univalent Functions Defined by Ruscheweyh DerivativesJay M. Jahangiri, S.R.Kulkarni, S. Shams경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2003 · 제43권 제4호Some subclasses of multivalent functions involving a certain linear operatorH. M. Srivastava, H. Silverman, M. K. Aouf장전수학회 · Advanced Studies in Contemporary Mathematics2007 · 제14권 제2호On Certain Subclasses of Meromorphically Univalent FuntionsJ. PATEL, POULASTI SAHOO경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2002 · 제42권 제1호On a Linear Combination of Classes of Multivalently Harmonic FunctionsJAY M. JAHANGIRI, OM P. AHUJA경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2002 · 제42권 제1호

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