A subclass of harmonic functions with varying arguments defined by Dziok-Srivastava operator

G. Murugusundaramoorthy; Kaliappan Vijaya; Ravinder Krishna Raina

Archivum Mathematicum (2009)

  • Volume: 045, Issue: 1, page 37-46
  • ISSN: 0044-8753

Abstract

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Making use of the Dziok-Srivastava operator, we introduce a new class of complex valued harmonic functions which are orientation preserving and univalent in the open unit disc and are related to uniformly convex functions. We investigate the coefficient bounds, distortion inequalities and extreme points for this generalized class of functions.

How to cite

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Murugusundaramoorthy, G., Vijaya, Kaliappan, and Raina, Ravinder Krishna. "A subclass of harmonic functions with varying arguments defined by Dziok-Srivastava operator." Archivum Mathematicum 045.1 (2009): 37-46. <http://eudml.org/doc/250557>.

@article{Murugusundaramoorthy2009,
abstract = {Making use of the Dziok-Srivastava operator, we introduce a new class of complex valued harmonic functions which are orientation preserving and univalent in the open unit disc and are related to uniformly convex functions. We investigate the coefficient bounds, distortion inequalities and extreme points for this generalized class of functions.},
author = {Murugusundaramoorthy, G., Vijaya, Kaliappan, Raina, Ravinder Krishna},
journal = {Archivum Mathematicum},
keywords = {harmonic univalent starlike functions; Dziok-Srivastava operator; distortion bounds; extreme points; uniformly convex functions; harmonic univalent starlike function; Dziok-Srivastava operator; distortion bound; extreme point; uniformly convex function},
language = {eng},
number = {1},
pages = {37-46},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {A subclass of harmonic functions with varying arguments defined by Dziok-Srivastava operator},
url = {http://eudml.org/doc/250557},
volume = {045},
year = {2009},
}

TY - JOUR
AU - Murugusundaramoorthy, G.
AU - Vijaya, Kaliappan
AU - Raina, Ravinder Krishna
TI - A subclass of harmonic functions with varying arguments defined by Dziok-Srivastava operator
JO - Archivum Mathematicum
PY - 2009
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 045
IS - 1
SP - 37
EP - 46
AB - Making use of the Dziok-Srivastava operator, we introduce a new class of complex valued harmonic functions which are orientation preserving and univalent in the open unit disc and are related to uniformly convex functions. We investigate the coefficient bounds, distortion inequalities and extreme points for this generalized class of functions.
LA - eng
KW - harmonic univalent starlike functions; Dziok-Srivastava operator; distortion bounds; extreme points; uniformly convex functions; harmonic univalent starlike function; Dziok-Srivastava operator; distortion bound; extreme point; uniformly convex function
UR - http://eudml.org/doc/250557
ER -

References

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  3. Clunie, J., Sheil-Small, T., Harmonic univalent functions, Ann. Acad. Sci. Fenn. Math. 9 (1984), 3–25. (1984) Zbl0506.30007MR0752388
  4. Dziok, J., Srivastava, H. M., 10.1080/10652460304543, Integral Transform. Spec. Funct. 14 (2003), 7–18. (2003) Zbl1040.30003MR1949212DOI10.1080/10652460304543
  5. Goodman, A. W., On uniformly convex functions, Ann. Polon. Math. 1991 (56), 87–92. (1956) MR1145573
  6. Jahangiri, J. M., Silverman, H., Harmonic univalent functions with varying rrguments, Int. J. Appl. Math. 8 (3) (2002), 267–275. (2002) MR1898507
  7. Murugusundaramoorthy, G., A class of Ruscheweyh-Type harmonic univalent functions with varying arguments, Southwest J. Pure Appl. Math. 2 (2003), 90–95. (2003) Zbl1050.30010MR2052983
  8. Rønning, F., Uniformly convex functions and a corresponding class of starlike functions, Proc. Amer. Math. Soc. 118 (1993), 189–196. (1993) MR1128729
  9. Rosy, T., Stephen, B. A., Subramanian, K. G., Jahangiri, J. M., Goodman-Ronning type harmonic univalent functions, Kyungpook Math. J. 41 (2001), 45–54. (2001) Zbl0988.30012MR1847436
  10. Ruscheweyh, S., 10.1090/S0002-9939-1975-0367176-1, Proc. Amer. Math. Soc. 49 (1975), 109–115. (1975) Zbl0303.30006MR0367176DOI10.1090/S0002-9939-1975-0367176-1
  11. Ruscheweyh, S., 10.1090/S0002-9939-1981-0601721-6, Proc. Amer. Math. Soc. 81 (1981), 521–528. (1981) Zbl0458.30008MR0601721DOI10.1090/S0002-9939-1981-0601721-6
  12. Srivastava, H. M., Owa, S., Some characterization and distortion theorems involving fractional calculus, generalized hypergeometric functions, Hadamard products, linear operators and certain subclasses of analytic functions, Nagoya Math. J. 106 (1998), 1–28. (1998) MR0894409
  13. Vijaya, K., Studies on certain subclasses of harmonic functions, Ph.D. thesis, VIT University, 2006. (2006) 

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