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Third-order differential subordination and superordination involving a fractional operator

Rabha W. Ibrahim;  Muhammad Zaini Ahmad;  Hiba F. Al-Janaby — 2015

Open Mathematics

The third-order differential subordination and the corresponding differential superordination problems for a new linear operator convoluted the fractional integral operator with the Carlson-Shaffer operator, are investigated in this study. The new operator satisfies the required first-order differential recurrence (identity) relation. This property employs the subordination and superordination methodology. Some classes of admissible functions are determined, and these significant classes are exploited...

Upper and lower bounds of integral operator defined by the fractional hypergeometric function

Rabha W. Ibrahim;  Muhammad Zaini Ahmad;  Hiba F. Al-Janaby — 2015

Open Mathematics

In this article, we impose some studies with applications for generalized integral operators for normalized holomorphic functions. By using the further extension of the extended Gauss hypergeometric functions, new subclasses of analytic functions containing extended Noor integral operator are introduced. Some characteristics of these functions are imposed, involving coefficient bounds and distortion theorems. Further, sufficient conditions for subordination and superordination are illustrated.

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