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Generalization of functions of bounded Mocanu variation with respect to 2k-symmetric conjugate points

Year 2020, Volume: 49 Issue: 3, 1206 - 1215, 02.06.2020
https://doi.org/10.15672/hujms.466909

Abstract

In this paper, by using convolution we generalize the class of analytic functions of bounded Mocanu variation with respect to 2k-symmetric conjugate points and study some of its basic properties. Our results generalize many research works in the literature.

References

  • [1] J. Dziok and K.I. Noor, Classes of analytic functions related to a combination of two convex functions, J. Math. Inequal. 11 (2), 413–427, 2017.
  • [2] J. Dziok, Characterizations of analytic functions associated with functions of bounded variation, Ann. Pol. Math. 109, 199–207, 2013.
  • [3] J. Dziok, Classes of functions associated with bounded Mocanu variation, J. Inequal. Appl. 2013, Art. No. 349, 2013.
  • [4] S.S. Miller and P.T. Mocanu, Differential Subordinations Theory and Applications, Marcel Dekker Inc, New York, 2000.
  • [5] K.I. Noor and S. Mustafa, Some classes of analytic functions related with functions of bounded radius rotation with respect to symmetrical points, J. Math. Inequal. 3 (2), 267–276, 2009.
  • [6] K.I. Noor and S. Hussain, On certain analytic functions associated with Ruscheweyh derivatives and bounded Mocanu variation, J. Math. Anal. Appl. 340 (2), 1145–1152, 2008.
  • [7] K.I. Noor, On subclasses of close-to-convex functions of higher order, Inter. J. Math. Math. Sci. 15, 279–290, 1992.
  • [8] K.I. Noor and S.N. Malik, On generalized bounded Mocanu variation associated with conic domain, Math. Comput. Modelling. 55 (3-4), 844–852, 2012.
  • [9] K.I. Noor and A. Muhammad, On analytic functions with generalized bounded Mocanu variation, Appl. Math. Comput. 196 (2), 802–811, 2008.
  • [10] G. Kohr, Geometric function theory in one and higher dimensions, Marcel Dekker Inc, New York, 2003.
  • [11] R. Parvatham and S. Radha, On α-starlike and α-close-to-convex functions with respect to n-symetric points, Indian J. Pure Appl. Math. 16 (9), 1114–1122, 1986.
  • [12] K. Padmanabhan and R. Parvatham, Properties of a class of functions with bounded boundary rotation, Ann. Polon. Math. 31, 311–323, 1975.
  • [13] B. Pinchuk, Functions with bounded boundary rotation, Isr. J. Math. 10, 7–16, 1971.
  • [14] S. Ruscheweyh, Convolutions in Geometric Function Theory. Sem. Math. Sup. 83, Presses de l’Université de Montréal, Montreal, 1982.
  • [15] Z.-G. Wang, C.-Y. Gao, and S.-M. Yuan, On certain subclasses of close-to-convex and quasi-convex functions with respect to k-symmetric points, J. Math. Anal. Appl. 322, 97–106, 2006.
  • [16] Z.-G. Wang and C.-Y. Gao, On starlike and convex functions with respect to 2ksymmetric conjugate points, Tamsui Oxf. J. Math. Sci. 24, 277–287, 2008.
  • [17] Z.-G. Wang and Y.-P. Jiang, Some properties of certain subclasses of close-to-convex and guasi-convex functions with respect to 2k-symmetric conjugate points, Bull. Iran. Math. Soc. 36 (2), 217–238, 2010.
  • [18] S.M. Yuan and Z.M. Liu, Some propertis of α-convex and α-quasiconvex functions with respect to n-symetric points, Appl. Math. Comput. 188 (2), 1142–1150, 2007.
Year 2020, Volume: 49 Issue: 3, 1206 - 1215, 02.06.2020
https://doi.org/10.15672/hujms.466909

Abstract

References

  • [1] J. Dziok and K.I. Noor, Classes of analytic functions related to a combination of two convex functions, J. Math. Inequal. 11 (2), 413–427, 2017.
  • [2] J. Dziok, Characterizations of analytic functions associated with functions of bounded variation, Ann. Pol. Math. 109, 199–207, 2013.
  • [3] J. Dziok, Classes of functions associated with bounded Mocanu variation, J. Inequal. Appl. 2013, Art. No. 349, 2013.
  • [4] S.S. Miller and P.T. Mocanu, Differential Subordinations Theory and Applications, Marcel Dekker Inc, New York, 2000.
  • [5] K.I. Noor and S. Mustafa, Some classes of analytic functions related with functions of bounded radius rotation with respect to symmetrical points, J. Math. Inequal. 3 (2), 267–276, 2009.
  • [6] K.I. Noor and S. Hussain, On certain analytic functions associated with Ruscheweyh derivatives and bounded Mocanu variation, J. Math. Anal. Appl. 340 (2), 1145–1152, 2008.
  • [7] K.I. Noor, On subclasses of close-to-convex functions of higher order, Inter. J. Math. Math. Sci. 15, 279–290, 1992.
  • [8] K.I. Noor and S.N. Malik, On generalized bounded Mocanu variation associated with conic domain, Math. Comput. Modelling. 55 (3-4), 844–852, 2012.
  • [9] K.I. Noor and A. Muhammad, On analytic functions with generalized bounded Mocanu variation, Appl. Math. Comput. 196 (2), 802–811, 2008.
  • [10] G. Kohr, Geometric function theory in one and higher dimensions, Marcel Dekker Inc, New York, 2003.
  • [11] R. Parvatham and S. Radha, On α-starlike and α-close-to-convex functions with respect to n-symetric points, Indian J. Pure Appl. Math. 16 (9), 1114–1122, 1986.
  • [12] K. Padmanabhan and R. Parvatham, Properties of a class of functions with bounded boundary rotation, Ann. Polon. Math. 31, 311–323, 1975.
  • [13] B. Pinchuk, Functions with bounded boundary rotation, Isr. J. Math. 10, 7–16, 1971.
  • [14] S. Ruscheweyh, Convolutions in Geometric Function Theory. Sem. Math. Sup. 83, Presses de l’Université de Montréal, Montreal, 1982.
  • [15] Z.-G. Wang, C.-Y. Gao, and S.-M. Yuan, On certain subclasses of close-to-convex and quasi-convex functions with respect to k-symmetric points, J. Math. Anal. Appl. 322, 97–106, 2006.
  • [16] Z.-G. Wang and C.-Y. Gao, On starlike and convex functions with respect to 2ksymmetric conjugate points, Tamsui Oxf. J. Math. Sci. 24, 277–287, 2008.
  • [17] Z.-G. Wang and Y.-P. Jiang, Some properties of certain subclasses of close-to-convex and guasi-convex functions with respect to 2k-symmetric conjugate points, Bull. Iran. Math. Soc. 36 (2), 217–238, 2010.
  • [18] S.M. Yuan and Z.M. Liu, Some propertis of α-convex and α-quasiconvex functions with respect to n-symetric points, Appl. Math. Comput. 188 (2), 1142–1150, 2007.
There are 18 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Rasoul Aghalary 0000-0001-8431-1735

Jafar Kazemzadeh This is me 0000-0002-6887-2759

Publication Date June 2, 2020
Published in Issue Year 2020 Volume: 49 Issue: 3

Cite

APA Aghalary, R., & Kazemzadeh, J. (2020). Generalization of functions of bounded Mocanu variation with respect to 2k-symmetric conjugate points. Hacettepe Journal of Mathematics and Statistics, 49(3), 1206-1215. https://doi.org/10.15672/hujms.466909
AMA Aghalary R, Kazemzadeh J. Generalization of functions of bounded Mocanu variation with respect to 2k-symmetric conjugate points. Hacettepe Journal of Mathematics and Statistics. June 2020;49(3):1206-1215. doi:10.15672/hujms.466909
Chicago Aghalary, Rasoul, and Jafar Kazemzadeh. “Generalization of Functions of Bounded Mocanu Variation With Respect to 2k-Symmetric Conjugate Points”. Hacettepe Journal of Mathematics and Statistics 49, no. 3 (June 2020): 1206-15. https://doi.org/10.15672/hujms.466909.
EndNote Aghalary R, Kazemzadeh J (June 1, 2020) Generalization of functions of bounded Mocanu variation with respect to 2k-symmetric conjugate points. Hacettepe Journal of Mathematics and Statistics 49 3 1206–1215.
IEEE R. Aghalary and J. Kazemzadeh, “Generalization of functions of bounded Mocanu variation with respect to 2k-symmetric conjugate points”, Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 3, pp. 1206–1215, 2020, doi: 10.15672/hujms.466909.
ISNAD Aghalary, Rasoul - Kazemzadeh, Jafar. “Generalization of Functions of Bounded Mocanu Variation With Respect to 2k-Symmetric Conjugate Points”. Hacettepe Journal of Mathematics and Statistics 49/3 (June 2020), 1206-1215. https://doi.org/10.15672/hujms.466909.
JAMA Aghalary R, Kazemzadeh J. Generalization of functions of bounded Mocanu variation with respect to 2k-symmetric conjugate points. Hacettepe Journal of Mathematics and Statistics. 2020;49:1206–1215.
MLA Aghalary, Rasoul and Jafar Kazemzadeh. “Generalization of Functions of Bounded Mocanu Variation With Respect to 2k-Symmetric Conjugate Points”. Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 3, 2020, pp. 1206-15, doi:10.15672/hujms.466909.
Vancouver Aghalary R, Kazemzadeh J. Generalization of functions of bounded Mocanu variation with respect to 2k-symmetric conjugate points. Hacettepe Journal of Mathematics and Statistics. 2020;49(3):1206-15.