On a Certain Subclass of Meromorphic Functions Defined by a New Linear Differential Operator
In this article, a new linear differential operator I^k (L_s^a (a_l,b_m )f(z)) is defined by using the Hadamard product of the q-hypergeometric function and a function related to the Hurwitz-Lerch zeta function. By using this linear differential operator, a new subclass L_(s,a)^(k,*) (α_l,β_m;A,B,b) of meromorphic functions is defined. Some properties and characteristics of this subclass are considered. These include the coefficient inequalities, the growth and distortion properties and the radii of meromorphic starlikeness and meromorphic convexity. Finally, closure theorems and extreme points are introduced.
Srivastava, H.M., Gaboury, S. & Ghanim, F., Certain Subclasses of Meromorphically Univalent Functions Defined by A Linear Operator Associated with the λ-generalized Hurwitz-Lerch Zeta Function, Integral Transforms and Special Functions, 26(4), pp. 258-272, 2015.
Wang, Z.G., Srivastava, H.M. & Yuan, S.M., Some Basic Properties of Certain Subclasses of Meromorphically Starlike Function, Journal of Inequalities and Applications, 2014(1), pp. 1-13, 2014.
Aldweby, H. & Darus, M., Integral Operator Defined by q-analogue of Liu-Srivastava Operator, Studio Universitatis Babes-Bolyai, Mathematica, 58(4), 2013.
Murugusundaramoorthy, G. & Janani, T., Meromorphic Parabolic Starlike Functions Associated with Hypergeometric Series, ISRN Mathematical Analysis, 2014, 2014.
Ghanim, F., A Study of a Certain Subclass of Hurwitz-Lerch Zeta Function Related to A Linear Operator, Abstract and Applied Analysis, volume 2013 (2013), Article ID 763756, 7 pages DOI:10.1155/2013 /763756.
Ghanim, F., Certain Properties of Classes of Meromorphic Functions Defined by A Linear Operator and Associated with Hurwitz-Lerch Zeta Function, Advanced Studies in Contemporary Mathematics, 27(2), pp. 175-180, 2017.
Srivastava, H.M. & Choi, J., Series Associated with Zeta and Related Functions, A New Book, Journal of Applied Mathematics and Stochastic Analysis, 15(1), pp. 97-97, 2002.
Srivastava, H.M. & Junesang, C., Zeta and q-zeta Functions and Associated Series and Integrals, 1st Ed., Elsevier, 2012.
Srivastava, H.M., Gaboury, S. & Ghanim, F., Some Further Properties of A Linear Operator Associated with the λ-generalized Hurwitz-Lerch Zeta Function Related to the Class of Meromorphically Univalent Functions, Applied Mathematics and Computation, 259, pp. 1019-1029, 2015.
Challab, K., Darus, M. & Ghanim, F., Certain Problems Related to Generalized Srivastava-Attiya Operator, Asian-European Journal of Mathematics, 1750027, 2016.
Srivastava, H.M., Some Formulas for the Bernoulli and Euler Polynomials at Rational Arguments, In Mathematical Proceedings of the Cambridge Philosophical Society, Cambridge University Press, 129, pp. 77-84, 2000.
Dziok, J. & Srivastava, H.M., Certain Subclasses of Analytic Functions Associated with the Generalized Hypergeometric Function, Integral Transforms and Special Functions, 14(1), pp. 7-18, 2003.
Ghanim, F. & Darus, M., Inclusion Properties for a Class of Meromorphic Functions Defined by A Linear Operator, J.Math.Fund.Sci., 48(3), pp. 276-284, 2016.
Ghanim, F. & Darus, M., New Subclass of Multivalent Hypergeometric Meromorphic Functions, International Journal of Pure and Applied Mathematics, 61(3), pp. 269-280, 2010.
Ghanim, F. & Darus, M., Some Properties of Certain Subclass of Meromorphically Multivalent Functions Defined by Linear Operator, Journal of Mathematics and Statistics, 6(1), pp. 34-41, 2010.
Ghanim, F. & Darus, M., A New Class of Meromorphically Analytic Functions with Applications to the Generalized Hypergeometric Functions, Abstract and Applied Analysis, 2011, Article ID 159405, 2011. DOI:10.1155/2011/159405
Liu, J.L. & Srivastava, H.M., Certain Properties of the Dziok-Srivastava Operator, Applied Mathematics and Computation, 159(2), pp. 485-493, 2004.
Liu, J.L. & Srivastava, H.M., Classes of Meromorphically Multivalent Functions Associated with the Generalized Hypergeometric Function, Mathematical and Computer Modelling, 39(1), pp. 21-34, 2004.
Ghanim, F. & Darus, M., Linear operators associated with a subclass of hypergeometric meromorphic uniformly convex functions, Acta Universitatis Apulensis, 17, pp. 49-60, 2009.
Challab, H. & Darus, M., On Certain Class of Meromorphic Harmonic Concave Functions Defined by Salagean Operator, Journal of Quality Measurement and Analysis, 11(1), pp. 49-60, 2015.
El-Ashwah, R.M., Aouf, M.K., & El-Deeb, S.M., Some Properties of Certain Subclasses of Meromorphic Multivalent Functions of Complex Order Defined by Certain Linear Operator, Acta Universitatis Apulensis, 40, pp. 265-282, 2014.
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