Main differential sandwich theorem with some applications

Oqlah Al-Refai, Maslina Darus

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

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: βzq1 k(z) q̀1(z) + ∑j=0 n αj q1 j(z) ≺ βzpk(z)p̀(z) + ∑j=0 n αj pj(z) ≺ βzq2 k(z)q̀2(z) + ∑j=0 n αj q2 j(z)implies q1(z) ≺ p(z) ≺ q2(z), where k∈ ℤ and β ≠ 0, ὰj s ∈ ℂ. Some of its special cases and its applications will be considered for certain analytic functions and certain linear operators.

Original languageEnglish
Pages (from-to)1-11
Number of pages11
JournalLobachevskii Journal of Mathematics
Volume30
Issue number1
DOIs
Publication statusPublished - Jan 2009

Fingerprint

Sandwich
Analytic function
Differential Superordination
Differential Subordination
Theorem
Linear Operator
First-order
Imply
Sufficient Conditions
Generalization

Keywords

  • Differential subordinations
  • Differential superordinations
  • Dominant
  • Subordinant

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Main differential sandwich theorem with some applications. / Al-Refai, Oqlah; Darus, Maslina.

In: Lobachevskii Journal of Mathematics, Vol. 30, No. 1, 01.2009, p. 1-11.

Research output: Contribution to journalArticle

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