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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...

On a class of starlike functions defined in a halfplane

G. Dimkov, J. Stankiewicz, Z. Stankiewicz (1991)

Annales Polonici Mathematici

Let D = z: Re z < 0 and let S*(D) be the class of univalent functions normalized by the conditions l i m D z ( f ( z ) - z ) = a , a a finite complex number, 0 ∉ f(D), and mapping D onto a domain f(D) starlike with respect to the exterior point w = 0. Some estimates for |f(z)| in the class S*(D) are derived. An integral formula for f is also given.

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