×

Generalizations of multivalent Mocanu functions. (English) Zbl 1410.30008

Summary: In the paper we generalize the class of multivalent Mocanu functions. The main object is to obtain characterizations and inclusion properties for defined classes of functions. Some applications of the main results to classes defined by the Srivastava-Wright operator are also considered.

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
30C50 Coefficient problems for univalent and multivalent functions of one complex variable
30C55 General theory of univalent and multivalent functions of one complex variable
33C20 Generalized hypergeometric series, \({}_pF_q\)
Full Text: DOI

References:

[1] Aouf, M. K., Some inclusion relationships associated with Dziok-Srivastava operator, Appl. Math. Comput., 216, 431-437 (2010) · Zbl 1186.30008
[2] 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, 470-483 (2004) · Zbl 1059.30006
[3] Coonce, H. B.; Ziegler, M. R., Functions with bounded Mocanu variation, Rev. Roum. Math. Pures Appl., 19, 1093-1104 (1974) · Zbl 0363.30010
[4] Dziok, J., Applications of multivalent prestarlike functions, Appl. Math. Comput., 221, 230-238 (2013) · Zbl 1329.30010
[5] Dziok, J., Characterizations of analytic functions associated with functions of bounded variation, Ann. Polon. Math., 109, 199-207 (2013) · Zbl 1291.30071
[6] Dziok, J., Inclusion relationships between classes of functions defined by subordination, Ann. Polon. Math., 100, 193-202 (2011) · Zbl 1216.30006
[7] Dziok, J., On the convex combination of the Dziok-Srivastava operator, Appl. Math. Comput., 188, 2, 1214-1220 (2007) · Zbl 1124.33007
[8] Dziok, J.; Srivastava, H. M., Certain subclasses of analytic functions associated with the generalized hypergeometric function, Integral Transforms Spec. Funct., 14, 7-18 (2003) · Zbl 1040.30003
[9] Dziok, J.; Srivastava, H. M., Classes of analytic functions associated with the generalized hypergeometric function, Appl. Math. Comput., 103, 1-13 (1999) · Zbl 0937.30010
[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, 289-305 (1978) · Zbl 0367.34005
[11] Hallenbeck, D. J.; MacGregor, T. H., Linear Problems and Convexity Techniques in Geometric Function Theory (1984), Pitman Advanced Publishing Program: Pitman Advanced Publishing Program Boston, Pitman · Zbl 0581.30001
[12] Kiryakova, V., Criteria for univalence of the Dziok-Srivastava and the Srivastava-Wright operators in the class \(A\), Appl. Math. Comput., 218, 883-892 (2011) · Zbl 1227.30012
[13] Liu, J.-L.; Noor, K. I., On subordinations for certain analytic functions associated with Noor integral operator, Appl. Math. Comput., 187, 1453-1460 (2007) · Zbl 1116.30008
[14] Mocanu, P. T., Une propriété de convexité g énéralisée dans la théorie de la représentation conforme, Math. (Cluj), 11, 127-133 (1969), (in French) · Zbl 0195.36401
[15] Noor, K. I.; Hussain, S., On certain analytic functions associated with Ruscheweyh derivatives and bounded Mocanu variation, J. Math. Anal. Appl., 340, 1145-1152 (2008) · Zbl 1155.30007
[16] Noor, K. I.; Malik, S. N., On generalized bounded Mocanu variation associated with conic domain, Math. Comput. Model., 55, 844-852 (2012) · Zbl 1255.30022
[17] Noor, K. I.; Muhammad, A., On analytic functions with generalized bounded Mocanu variation, Appl. Math. Comput., 196, 2, 802-811 (2008) · Zbl 1133.30309
[18] Noor, K. I.; Ul-Haq, W., On some implication type results involving generalized bounded Mocanu variations, Comput. Math. Appl., 63, 10, 1456-1461 (2012) · Zbl 1247.30025
[19] Paatero, V., Über die konforme Abbildung von Gebieten deren Ränder von beschränkter Drehung sind, Ann. Acad. Sei. Fenn. Ser A, 33, 1-79 (1931) · Zbl 0005.25104
[20] Patel, J.; Mishra, A. K.; Srivastava, H. M., Classes of multivalent analytic functions involving the Dziok-Srivastava operator, Comput. Math. Appl., 54, 599-616 (2007) · Zbl 1155.30332
[21] Padmanabhan, K.; Parvatham, R., Properties of a class of functions with bounded boundary rotation, Ann. Polon. Math., 31, 311-323 (1975) · Zbl 0337.30009
[22] Piejko, K.; Sokół, J., On the Dziok-Srivastava operator under multivalent analytic functions, Appl. Math. Comput., 177, 839-843 (2006) · Zbl 1100.30018
[23] Pinchuk, B., Functions with bounded boundary rotation, Isr. J. Math., 10, 7-16 (1971) · Zbl 0224.30024
[24] Ruscheweyh, S., Linear operators between classes of prestarlike functions, Commun. Math. Helv., 52, 497-509 (1977) · Zbl 0372.30007
[25] Srivastava, H. M., Some Fox-Wright generalized hypergeometric functions and associated families of convolution operators, Appl. Anal. Discrete Math., 1, 56-71 (2007) · Zbl 1224.30084
[26] Srivastava, H. M.; Lashin, A. Y., Subordination properties of certain classes of multivalently analytic functions, Math. Comput. Model., 52, 596-602 (2010) · Zbl 1201.30019
[27] Supramaniam, S.; Ali, R. M.; Lee, S. K.; Ravichandran, V., Convolution and differential subordination for multivalent functions, Bull. Malays. Math. Sci. Soc., 32, 351-360 (2009) · Zbl 1176.30065
[28] Wang, Z.-G.; Zhang, G.-W.; Wen, F.-H., Properties and characteristics of the Srivastava-Khairnar-More integral operator, Appl. Math. Comput., 218, 7747-7758 (2012) · Zbl 1244.45006
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.