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On a class of analytic functions generated by fractional integral operator

Rabha W. Ibrahim — 2017

Concrete Operators

In this note, we improve the idea of the Tsallis entropy in a complex domain. This improvement is contingent on the fractional operator in a complex domain (type Alexander). We clarify some new classes of analytic functions, which are planned in view of the geometry function theory. This category of entropy is called fractional entropy; accordingly, we demand them fractional entropic geometry classes. Other geometric properties are established in the sequel. Our exhibition is supported by the Maxwell...

Third-order differential subordination and superordination involving a fractional operator

Rabha W. IbrahimMuhammad Zaini AhmadHiba 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. IbrahimMuhammad Zaini AhmadHiba 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.

Inequalities of harmonic univalent functions with connections of hypergeometric functions

Janusz SokółRabha W. IbrahimM. Z. AhmadHiba F. Al-Janaby — 2015

Open Mathematics

Let SH be the class of functions f = h+g that are harmonic univalent and sense-preserving in the open unit disk U = { z : |z| < 1} for which f (0) = f'(0)-1=0. In this paper, we introduce and study a subclass H( α, β) of the class SH and the subclass NH( α, β) with negative coefficients. We obtain basic results involving sufficient coefficient conditions for a function in the subclass H( α, β) and we show that these conditions are also necessary for negative coefficients, distortion bounds, extreme...

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