Main differential sandwich theorem with some applications

Autor: Oqlah Al-Refai, Maslina Darus
Rok vydání: 2009
Předmět:
Zdroj: Lobachevskii Journal of Mathematics. 30:1-11
ISSN: 1818-9962
1995-0802
DOI: 10.1134/s1995080209010016
Popis: Let q1, q2 be univalent in Δ:= {z: |z| < 1} and p be certain analytic function. We give some applications of first order differential subordinations and superordinations to obtain sufficient conditions to satisfy the following sandwich implication which is a generalization for various known sandwich theorems: $$ \beta zq_1^k (z)q'_1 (z) + \sum\limits_{j = 0}^n {\alpha _j q_1^j (z)} \prec \beta zp^k (z)p'(z) + \sum\limits_{j = 0}^n {\alpha _j p^j (z)} \prec \beta zq_2^k (z)q'_2 (z) + \sum\limits_{j = 0}^n {\alpha _j q_2^j (z)} $$ implies q1(z) ≺ p(z) ≺ q2(z), where k ∈ ℤ and β ≠ 0, α′j ∈ ℂ. Some of its special cases and its applications will be considered for certain analytic functions and certain linear operators.
Databáze: OpenAIRE
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