Startseite Mathematik Inclusion properties for classes of analytic functions associated with conic domains
Artikel
Lizenziert
Nicht lizenziert Erfordert eine Authentifizierung

Inclusion properties for classes of analytic functions associated with conic domains

  • Jacek Dziok EMAIL logo
Veröffentlicht/Copyright: 30. April 2016
Veröffentlichen auch Sie bei De Gruyter Brill
Informationen für Autor*innen Erkunden Sie dieses Fachgebiet
Mathematica Slovaca
Aus der Zeitschrift Mathematica Slovaca Band 66 Heft 1

Abstract

In the paper we define classes of functions associated with conic domains. Some characterizations and inclusion properties of these classes of functions are given.

Keywords: analytic functions; bounded variation; bounded boundary rotation; multivalent prestarlike functions
MSC: Primary 30C45; 30C50; 30C55

This work is partially supported by the Centre for Innovation and Transfer of Natural Sciences and Engineering Knowledge, University of Rzeszow.

  1. This paper has been communicated by Stanisława Kanas

Acknowledgement

The author would like to thank the referees for their valuable suggestions and comments.

References

[1] Aouf, M. K.: Some inclusion relationships associated with Dziok-Srivastava operator, Appl. Math. Comput. 216 (2010), 431–437.10.1016/j.amc.2010.01.034Suche in Google Scholar

[2] Bhargava, S.—Nanjunda, R. S.: Convexity of a class of functions related to classes of starlike functions and functions with boundary rotation, Ann. Polon. Math. 49 (1989), 229–235.10.4064/ap-49-3-229-235Suche in Google Scholar

[3] Cho, N. E.—Kwon, O. S.—Srivastava, H. M.: Inclusion relationships and argument properties for certain subclasses of multivalent functions associated with a family of linear operators, J. Math. Anal. Appl. 292 (2004), 470–483.10.1016/j.jmaa.2003.12.026Suche in Google Scholar

[4] Coonce, H. B.—Ziegler, M. R.: Functions with bounded Mocanu variation, Rev. Roumaine Math. Pures Appl. 19 (1974), 1093–1104.Suche in Google Scholar

[5] Dziok, J.: Applications of multivalent prestarlike functions, Appl. Math. Comput. 221 (2013), 230–238.10.1016/j.amc.2013.06.054Suche in Google Scholar

[6] Dziok, J.: Applications of the Jack lemma, Acta Math. Hungar. 105 (2004), 93–102.10.1023/B:AMHU.0000045533.37931.19Suche in Google Scholar

[7] Dziok, J.: Inclusion relationships between classes of functions defined by subordination, Ann. Polon. Math. 100 (2011), 193–202.10.4064/ap100-2-8Suche in Google Scholar

[8] Dziok, J.: Characterizations of analytic functions associated with functions of bounded variation, Ann. Polon. Math. 109 (2013), 199–207.10.4064/ap109-2-7Suche in Google Scholar

[9] Dziok, J.—Srivastava, H. M.: Certain subclasses of analytic functions associated with the generalized hypergeometric function, Integral Transforms Spec. Funct. 14 (2003), 7–18.10.1080/10652460304543Suche in Google Scholar

[10] Eenigenburg, P .J.—Miller, S. S.—Mocanu, P. T.—Reade, O. M.: Second order differential inequalities in the complex plane, J. Math. Anal. Appl. 65 (1978), 28–305.10.1016/0022-247X(78)90181-6Suche in Google Scholar

[11] Goodman, A. W.: On uniformly starlike functions, J. Math. Anal. Appl. 155 (1991), 364–370.10.1016/0022-247X(91)90006-LSuche in Google Scholar

[12] Kanas, S.: Techniques of the differential subordination for domains bounded by conic sections, Int. J. Math. Math. Sci. 38 (2003), 2389–2400.10.1155/S0161171203302212Suche in Google Scholar

[13] Kanas, S.—Sugawa, T.: On conformal representation of the interior of an ellipse, Ann. Acad. Sci. Fenn. Math. 31 (2006), 329–348.Suche in Google Scholar

[14] Kanas, S.—Wiśniowska, A.: Conic regions and k-uniform convexity, J. Comput. Appl. Math. 105 (1999), 327–336.10.1016/S0377-0427(99)00018-7Suche in Google Scholar

[15] Liu, J-L.—Noor, K. I.: On subordinations for certain analytic functions associated with Noor integral operator, Appl. Math. Comput. 187 (2007), 1453–1460.10.1016/j.amc.2006.09.061Suche in Google Scholar

[16] Hallenbeck, D. J.—MacGregor, T. H.: Linear Problems and Convexity Techniques in Geometric Function Theory. Pitman Advanced Publishing Program, Pitman, Boston, 1984.Suche in Google Scholar

[17] Moulis, E .J.: Generalizations of the Robertson functions, Pacific J. Math. 81 (1979), 167–174.10.2140/pjm.1979.81.167Suche in Google Scholar

[18] Noor, K. I.: On uniformly Bazilevic and related functions, Abstr. Appl. Anal. (2012), Art. ID 345261, 15 pp.10.1155/2012/345261Suche in Google Scholar

[19] Noor, K. I.—Hussain, S.: On certain analytic functions associated with Ruscheweyh derivatives and bounded Mocanu variation, J. Math. Anal. Appl. 340 (2008), 1145–1152.10.1016/j.jmaa.2007.09.038Suche in Google Scholar

[20] Noor, K. I.—Malik, S. N.: On generalized bounded Mocanu variation associated with conic domain, Math. Comput. Modelling 55 (2012), 844–852.10.1016/j.mcm.2011.09.012Suche in Google Scholar

[21] Noor, K. I.—Muhammad, A.: On analytic functions with generalized bounded Mocanu variation, Appl. Math. Comput. 196 (2008), 802–811.10.1016/j.amc.2007.07.017Suche in Google Scholar

[22] Noor, K. I.—Ul-Haq, W.: On some implication type results involving generalized bounded Mocanu variations, Comput. Math. Appl. 63 (2012), 1456–1461.10.1016/j.camwa.2012.03.055Suche in Google Scholar

[23] Paatero, V.: Über die konforme Abbildung von Gebieten deren Ränder von beschränkter Drehung sind, Ann. Acad. Sci. Fenn. Ser A 33 (1931), 1–79.10.1111/j.1749-6632.1931.tb55198.xSuche in Google Scholar

[24] Patel, J.—Mishra, A. K.—Srivastava, H. M.: Classes of multivalent analytic functions involving the Dziok–Srivastava operator, Comput. Math. Appl. 54 (2007), 599–616.10.1016/j.camwa.2006.08.041Suche in Google Scholar

[25] Padmanabhan, K.—Parvatham, R.: Properties of a class of functions with bounded boundary rotation, Ann. Polon. Math. 31 (1975), 311–323.10.4064/ap-31-3-311-323Suche in Google Scholar

[26] Piejko, K.—Sokół, J.: On the Dziok-Srivastava operator under multivalent analytic functions, Appl. Math. Comput. 177 (2006), 839–843.10.1016/j.amc.2005.11.039Suche in Google Scholar

[27] Pinchuk, B.: Functions with bounded boundary rotation, Israel J. Math. 10 (1971), 7–16.10.1007/BF02771515Suche in Google Scholar

[28] Ruscheweyh, S.: Linear operators between classes of prestarlike functions, Comment. Math. Helv. 52 (1977), 497–509.10.1007/BF02567382Suche in Google Scholar

[29] Sălăgean, G. S.: Subclasses of univalent functions. In: Lecture Notes in Math. 1013, Springer-Verlag, Berlin-Heidelberg, 1983, pp. 362–372.10.1007/BFb0066543Suche in Google Scholar

[30] Srivastava, H. M.—Lashin, A. Y.: Subordination properties of certain classes of multivalently analytic functions, Math. Comput. Modelling, 52 (2010), 596–602.10.1016/j.mcm.2010.04.005Suche in Google Scholar

[31] Wang, Z-G.—Zhang, G-W.—Wen, F-H.: Properties and characteristics of the Srivastava–Khairnar–More integral operator, Appl. Math. Comput. 218 (2012), 7747–7758.10.1016/j.amc.2012.01.038Suche in Google Scholar

Received: 2013-3-2
Accepted: 2013-8-23
Published Online: 2016-4-30
Published in Print: 2016-2-1

© 2016 Mathematical Institute Slovak Academy of Sciences

Artikel in diesem Heft

  1. Research Article
  2. Prof. RNDr. Ján Jakubík, DrSc. passed away
  3. Research Article
  4. On the number of slim, semimodular lattices
  5. Research Article
  6. Quantum computational algebra with a non-commutative generalization
  7. Research Article
  8. Lexico groups and direct products of lattice ordered groups
  9. Research Article
  10. Values of limit periodic sequences and functions
  11. Research Article
  12. On representation of quasi-Hopf group coalgebras
  13. Research Article
  14. On the q-Bernstein polynomials of the logarithmic function in the case q > 1
  15. Research Article
  16. On some modification of Darboux property
  17. Research Article
  18. Separating sets by peripherally continuous functions
  19. Research Article
  20. Persistence and extinction of a stochastic delay predator-prey model in a polluted environment
  21. Research Article
  22. On O’Malley preponderantly continuous functions
  23. Research Article
  24. Inequalities for the normalized Jensen functional with applications
  25. Research Article
  26. Majorization of starlike and convex functions of complex order involving linear operators
  27. Research Article
  28. Fekete–Szegö problem for some starlike functions related to shell-like curves
  29. Research Article
  30. Central functions for classes of concave univalent functions
  31. Research Article
  32. Inclusion properties for classes of analytic functions associated with conic domains
  33. Research Article
  34. Uniqueness of meromorphic functions and nonlinear differential polynomials sharing a nonzero polynomial
  35. Research Article
  36. Solutions and constrained null-controllability for a differential-difference equation
  37. Research Article
  38. Oscillation criteria for quasi-linear neutral delay dynamic equations on time scale
  39. Research Article
  40. Time periodic solutions for a sixth order nonlinear parabolic equation
  41. Research Article
  42. Some inequalities of trigonometric approximation in weighted Orlicz spaces
  43. Research Article
  44. Summation methods applied to Voronovskaya-type theorems for the partial sums of Fourier series and for Fejér operators
  45. Research Article
  46. Dichotomies for Orlicz spaces
  47. Research Article
  48. On freely generated semigraph C*-algebras
  49. Research Article
  50. Operators with a given part of the numerical range
  51. Research Article
  52. Characterization of quasi-continuity of multifunctions of two variables
  53. Research Paper
  54. Confidence regions in singular weakly nonlinear regression models with constraints
  55. Research Article
  56. Global stability of an SEI model for plant diseases
https://doi.org/10.1515/ms-2015-0125
Schlagwörter für diesen Artikel
analytic functions; bounded variation; bounded boundary rotation; multivalent prestarlike functions

Artikel in diesem Heft

  1. Research Article
  2. Prof. RNDr. Ján Jakubík, DrSc. passed away
  3. Research Article
  4. On the number of slim, semimodular lattices
  5. Research Article
  6. Quantum computational algebra with a non-commutative generalization
  7. Research Article
  8. Lexico groups and direct products of lattice ordered groups
  9. Research Article
  10. Values of limit periodic sequences and functions
  11. Research Article
  12. On representation of quasi-Hopf group coalgebras
  13. Research Article
  14. On the q-Bernstein polynomials of the logarithmic function in the case q > 1
  15. Research Article
  16. On some modification of Darboux property
  17. Research Article
  18. Separating sets by peripherally continuous functions
  19. Research Article
  20. Persistence and extinction of a stochastic delay predator-prey model in a polluted environment
  21. Research Article
  22. On O’Malley preponderantly continuous functions
  23. Research Article
  24. Inequalities for the normalized Jensen functional with applications
  25. Research Article
  26. Majorization of starlike and convex functions of complex order involving linear operators
  27. Research Article
  28. Fekete–Szegö problem for some starlike functions related to shell-like curves
  29. Research Article
  30. Central functions for classes of concave univalent functions
  31. Research Article
  32. Inclusion properties for classes of analytic functions associated with conic domains
  33. Research Article
  34. Uniqueness of meromorphic functions and nonlinear differential polynomials sharing a nonzero polynomial
  35. Research Article
  36. Solutions and constrained null-controllability for a differential-difference equation
  37. Research Article
  38. Oscillation criteria for quasi-linear neutral delay dynamic equations on time scale
  39. Research Article
  40. Time periodic solutions for a sixth order nonlinear parabolic equation
  41. Research Article
  42. Some inequalities of trigonometric approximation in weighted Orlicz spaces
  43. Research Article
  44. Summation methods applied to Voronovskaya-type theorems for the partial sums of Fourier series and for Fejér operators
  45. Research Article
  46. Dichotomies for Orlicz spaces
  47. Research Article
  48. On freely generated semigraph C*-algebras
  49. Research Article
  50. Operators with a given part of the numerical range
  51. Research Article
  52. Characterization of quasi-continuity of multifunctions of two variables
  53. Research Paper
  54. Confidence regions in singular weakly nonlinear regression models with constraints
  55. Research Article
  56. Global stability of an SEI model for plant diseases
Jetzt anmelden und 20% sparen
Institutioneller Zugang
Wie funktioniert Authentifizierung?
Haben Sie eine Idee, wie wir unsere Website verbessern können?
Bitte schreiben Sie uns.
© 2025 De Gruyter Brill
Heruntergeladen am 15.12.2025 von https://www.degruyterbrill.com/document/doi/10.1515/ms-2015-0125/pdf
Button zum nach oben scrollen