Skip to main content Accessibility help
×
Home

Univalent and Starlike Generalized Hypergeometric Functions

  • Shigeyoshi Owa (a1) and H. M. Srivastava (a2)

Extract

A single-valued function f(z) is said to be univalent in a domain if it never takes on the same value twice, that is, if f(z 1) = f(z 2) for implies that z 1 = z 2. A set is said to be starlike with respect to the line segment joining w 0 to every other point lies entirely in . If a function f(z) maps onto a domain that is starlike with respect to w 0, then f(z) is said to be starlike with respect to w 0. In particular, if w 0 is the origin, then we say that f(z) is a starlike function. Further, a set is said to be convex if the line segment joining any two points of lies entirely in . If a function f(z) maps onto a convex domain, then we say that f(z) is a convex function in .

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Univalent and Starlike Generalized Hypergeometric Functions
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Univalent and Starlike Generalized Hypergeometric Functions
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Univalent and Starlike Generalized Hypergeometric Functions
      Available formats
      ×

Copyright

References

Hide All
1. Carlson, B. C. and Shaffer, D. B., Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal. 75 (1984), 737745.
2. Duren, P. L., Univalent functions, Grundelheren der Mathematischen Wissenschaften 259 (Springer-Verlag, New York, Berlin, Heidelberg and Tokyo, 1983).
3. Jack, I. S., Functions starlike and convex of order a, J. London Math. Soc. (2) 3 (1971), 469474.
4. Lewis, J. L., Convexity of a certain series, J. London Math. Soc. (2) 27 (1983), 435446.
5. MacGregor, T. H., The radius of convexity for starlike functions of order 1/2, Proc. Amer. Math. Soc. 74(1963), 7176.
6. Merkes, E. P. and Scott, W. T., Starlike hyper geometric functions, Proc. Amer. Math. Soc. 72 (1961), 885888.
7. Owa, S., On the distortion theorems, I, Kyungpook Math. J. 18 (1978), 5359.
8. Pinchuk, B., On starlike and convex functions of order α, Duke Math. J. 35 (1968), 721734.
9. Robertson, M.S., On the theory of univalent functions, Ann. of Math. 37 (1936), 374408.
10. Ross, B., A brief history and exposition of the fundamental theory of fractional calculus, in Fractional calculus and its applications, (Springer-Verlag, Berlin, Heidelberg and New York, 1975), 136.
11. Ruscheweyh, S., Linear operators between classes of prestarlike functions, Comment. Math. Helv. 52 (1977), 497509.
12. Ruscheweyh, S. and Sheil-Small, T., Hadamard products of schlicht functions and the Pólya-Schoenberg conjecture, Comment. Math. Helv. 48 (1973), 119135.
13. Schild, A., On starlike functions of order α, Amer. J. Math. 87 (1965), 6570.
14. Singh, V., Bounds on the curvature of level lines under certain classes of univalent and locally univalent mappings, Indian J. Pure Appl. Math. 10 (1979), 129144.
15. Srivastava, H. M. and Owa, S., An application of the fractional derivative, Math. Japon. 29 (1984), 383389.
16. Srivastava, H. M., Owa, S. and Nishimoto, K., Some fractional differintegral equations, J. Math. Anal. Appl. 106 (1985), 360366.
17. Suffridge, T. J., Starlike functions as limits of polynomials, in Advances in complex function theory, (Springer-Verlag, Berlin, Heidelberg and New York, 1976), 164203.
18. Twomey, J. B., On starlike functions, Proc. Amer. Math. Soc. 24 (1970), 9597.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed