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
Rasoul Aghalary
,
Jafar Kazemzadeh
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
Rasoul Aghalary
,
Jafar Kazemzadeh
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.