Gbolagade, A. M.; Makinde, D. O. Operator on Hilbert space and its application to certain multivalent functions with fixed point associated with hypergeometric function. (English) Zbl 1357.30010 Tbil. Math. J. 9, No. 2, 151-157 (2016). Summary: By applying hypergeometric operator on Hilbert space, the author introduces a new class of meromorphic multivalent functions with an arbitrary fixed point omega. Properties such as coefficient inequalities, distortion bounds and extreme points were derived. Furthermore, the effect of this operator on functions in this class was also investigated. 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 Keywords:new class of meromorphic functions in the disk; distortion; coefficient estimates × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Acu Mugur and Shigeyoshi Owa, On some subclasses of univalent functions, Journal of In- equalities in Pure and Applied Mathematics, 6, No. 3, Article 70 (2005), 1-14.; · Zbl 1084.30009 [2] H. Aldweby and M. Darus, A subclass of hamonic univalent functions associated with q-analogue of Dziok-Srivastava operator, ISRN Math. Anal.2013, Art. ID 382312, 6pp.; · Zbl 1286.30002 [3] M. K. Aouf, A. Shamandy, A. O. Mostafa and S. M. Madian, A subclass of m - w starlike functions, Acta Universitatis Apulensis, No. 21, (2010), 135-142.; · Zbl 1212.30024 [4] R. Dunford and J. T. Schwartz, Linear operators, part 1, General Theory, New York - Lon- don,Interscience, 1985.; · Zbl 0635.47003 [5] H. Exton, q-hypergeometric functions and applications, Ellis Horwood Series: Mathematics and its application, Ellis Horwood, Chichester, UK, 1983.; · Zbl 0514.33001 [6] F. Fan, Analytic functions of a proper contractions, Math. Z, 160, (1978), 275-290.; · Zbl 0455.47013 [7] B. A. Frasin and M. Darus, On certain meromorphic functions with positive coefficients, South East Asian Bull. of Math., 28, (2004), 615-623.; · Zbl 1069.30016 [8] G. Gasper and M. Rahman, Basic hypergeometric series, Vol. 35 of Encyclopedia of Mathe- matics and its applications, Cambridge Unlversity Press, Cambridge, UK, 1990.; · Zbl 0695.33001 [9] F. Ghanim and M. Darus, On new subclass of analytic p-valent functions with negative coefficient for operator on Hilbert space, Int. Math. Forum, 3, No. 2 (2008), 69-77.; · Zbl 1159.30311 [10] S. B. Joshi, On a class of analytic functions with negative coefficient for operator on Hilbert space, J. App. Theory and Application, (1998), 107-112.; · Zbl 0974.30008 [11] S. Kanas and F. Ronning, Uniformly starlike and convex functions and other related classes of univalent functions, Ann. Univ. Mariae Curie-skldowska Section A, 53, (1999), 95-105.; · Zbl 0993.30008 [12] SH. Najafzadeh and A. Ebadian, Operator on Hilbert space and its application to certain univalent function with a fixed point, Acta Universitatis Apulensis, No. 27 (2011), 51-56.; · Zbl 1265.30083 [13] A. T. Oladipo, A. O. Fadipe-Joseph and B. O. Moses, On a new class of uniformly analytic functions associated with q-analogue of Dziok-Srivastava operator, Far East Journal of Mathe- matical Sciences, 89, No. 2 (2014), 153-167.; · Zbl 1307.30034 [14] A. T. Oladipo, On certain classes of analytic and univalent functions involving convolution operators, Acta Universitatis Apulensis, Math. Inform., No. 20 (2009), 163-174.; · Zbl 1224.30067 [15] A. T. Oladipo, On subclass of analytic and univalent functions, Advances in Applied Mathe- matical Analysis, 4, No. 1 (2009), 87-93.; [16] Y. Xiaopei, A subclass of analytic p-valent functions for operator on Hilbert space, Math. Japan, 40, (1984), 303-308.; · Zbl 0843.30019 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.