Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Concrete Operators

Ed. by Ross, William / Mashreghi, Javad

1 Issue per year


Mathematical Citation Quotient (MCQ) 2017: 0.34

Open Access
Online
ISSN
2299-3282
See all formats and pricing
More options …

On a class of analytic functions generated by fractional integral operator

Rabha W. Ibrahim
  • Corresponding author
  • Faculty of Computer Science and Information Technology, University Malaya, 50603, Malaya, Malaysia
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2017-01-31 | DOI: https://doi.org/10.1515/conop-2017-0001

Abstract

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 Lemma and Jack Lemma.

Keywords: Fractional calculus; Fractional entropy; Analytic function; Subordination and superordination

MSC 2010: 30C45

References

  • [1] R. W. Ibrahim, The fractional differential polynomial neural network for approximation of functions, Entropy 15.10, 4188 (2013).Web of ScienceGoogle Scholar

  • [2] R. W. Ibrahim, H. A. Jalab, Existence of entropy solutions for nonsymmetric fractional systems. Entropy 16.9, 4911 (2014).CrossrefWeb of ScienceGoogle Scholar

  • [3] J. W. Alexsander, Functions which map the interior of the unit circle upon simple regions, Annals. Math., 17, 12(1915).CrossrefGoogle Scholar

  • [4] S. S. Miller, P. T. Mocanu, Differential Subordinations : Theory and Applications, (Mrcel Dekker Inc., New York, 2000).Google Scholar

  • [5] A. W. Goodman, Univalent Functions, 2nd edition, (Mariner Publishing Co. Inc., 1983).Google Scholar

  • [6] S. S. Miller, P. T. Mocanu, M. O. Reade, Bazilevic functions and generalized convexity, Rev. Roumaine Math. Pure Appl. 19, 213 (1974).Google Scholar

  • [7] I. S. Jack, Functions starlike and convex of order , J.London Math. Soc. 3, 469(1971).CrossrefGoogle Scholar

  • [8] C. Tsallis, Generalized entropy-based criterion for consistent testing, Physical Review E, 58( 2) 1442 (1998Google Scholar

About the article

Received: 2016-11-02

Accepted: 2016-11-29

Published Online: 2017-01-31

Published in Print: 2017-01-26


Citation Information: Concrete Operators, Volume 4, Issue 1, Pages 1–6, ISSN (Online) 2299-3282, DOI: https://doi.org/10.1515/conop-2017-0001.

Export Citation

© 2017. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Rabha W. Ibrahim
Asian-European Journal of Mathematics, 2017, Page 1850013

Comments (0)

Please log in or register to comment.
Log in