Inclusion Attributes with Applications for Certain Subclasses of Analytic Subroutines

Vinod Kumar; Prachi Srivastava

doi:https://doi.org/10.14445/22315373/IJMTT-V37P508

International Journal of Mathematics Trends and Technology

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Volume 37 | Number 1 | Year 2016 | Article Id. IJMTT-V37P508 | DOI : https://doi.org/10.14445/22315373/IJMTT-V37P508

Inclusion Attributes with Applications for Certain Subclasses of Analytic Subroutines

Vinod Kumar, Prachi Srivastava

Abstract

Let A be the class of functions f analytical in the open unit disc E = {z: |z|< 1} and are normalized with the condition f(0) = 0, f’(0) = 1. Also let S.S * (γ). C(γ) announce the subclasses of A comprising of function that are severally monovalent star like of order γ and convex of order γ, 0 ≤ γ < 1. In E.

Keywords

Let A be the class of functions f analytical in the open unit disc E = {z: |z|< 1} and are normalized with the condition f(0) = 0, f’(0) = 1.

References

[1] S. D. Bernardi, Convex and starlike univalent functions, Trans. Amer. Math. Soc. 135 (1969) 429-446.
[2] B. C. Carlson, B. B. Shaffer, Starlike and prestart like hypergeometric functions, SIAM J. Math. Anal, 159 (1984) 737- 745.
[3] J. H. Choi, M. Saigo, H. M. Srivastava, Some inclusion properties of a certain family of integral operators, J. Math. Anal. Appl. 276 (2002), 432-445.
[4] P. Eenigenburg, P. T. Mocanu, S. S. Miller, M. O. Reade, On a Briot-Bouquet differential subordination in General inequalities, 64 (1983), Internationale Schriftenreihe Numerischen Mathematik, 329-348, Birkhauser, Basel, Switzerland.
[5] T. M. Flett, The dual of an inequality of Hardy and Littelwood and some related inequalities, J. Math. Anal. Appl. 38 (1972), 746-765.
[6] A. W. Goodman, Univalent Functions, I,II, Polygonal Publishing House, Washington, New Jersey, (1983).
[7] D. J. Hallenbeck, T. H. MacGregor, Linear problems and convexity techniques in geometric function theory, Pitman Publ. Ltd., London, (1984).
[8] I. B. Jung, Y. C. Kim, H. M. Srivastava, The Hardy space of analytic functions associated with certain one-parameter families of integral operators, J. Math. Anal. Appl. 176 (1993), 138- 147.
[9] S. Kanas, Techniques of differential subordination for domains bounded by conic sections, Internat. J. Math. Math. Sci. 38 (2003), 2389-2400.
[10] S. Kanas, A. Wisniowska, Conic regions and k-uniform convexity, J. Comput. Appl. Math. 105 (1999), 327-336.
[11] J-L. Liu, K. I. Noor, On subordinations for certain analytic functions associated with Noor Integral operator, Appl. Math. Compu. 187 (2007), 1453-1460.
[12] S. S. Miller, P. T. Mocanu, Differential Subordination Theory and Applications, Marcel Dekker Inc., New York, Basel, (2000).
[13] Z. Nehari, E. Netanyohu, On the coefficients of meromorphic schlicht functions, Proc. Amer. Math. Soc. 8, (1957), 15-23.
[14] K. I. Noor, On some applications of certain integral operators, Appl. Math. Comput. 188 (2007), 814-823.
[15] K. I. Noor, On a generalization of uniformaly convex and related functions, Comput. Math. Appl. 61 (2011), 117-125.
[16] K. I. Noor, Some classes of p-analytic functions defined by certain integral operator, Math. Inequal. Appl., 9 (2006), 117-123.
[17] K. I. Noor, Applications of certain operators to the classes of analytic functions related with generalized conic domains, Comut. Math. Appl. 62 (2011), 4194-4206.
[18] K. I. Noor, On generalizations of uniformly convex and related functions, Comput. Math. Appl. 61 (2011), 117-125.
[19] K. I. Noor, M. A. Noor, On integral operators, J. Math. Anal. Appl. 238 (1999), 341-352.
[20] K. I. Noor, M. A. Noor, Higher-order close-to-convex functions related with conic domain, Appl. Math. Inform. Sci. 8, (2014).
[21] K. I. Noor, M. Arif, W. Ul-Haq, On k-uniformly close-to-convex functions of complex order, Appl. Math. Comput. 215, (2009) 629-635.
[22] K. I. Noor, R. Fayyaz, M. A. Noor, Some classes of kuniformly functions with bounded radius rotation, Appl. Math. Inform. Sci. 8 (2014), 527-533.
[23] K. I. Noor, W. Ul-Haq, M. Arif, S. Mustafa, On bounded boundary and bounded radius rotation, J. Inequal. Appl. 2009 (2009), Article ID 813687, 12 pages.
[24] Ch. Pommerenke, Univalent Functions, Vanderhoeck and Ruprecht, Gottengen, (1975).
[25] S. Ruscheweyh, Convolutions in Geometric Function Theory, Les Presse de universite de Montreal, Montreal, (1982).
[26] S. Ruscheweyh, New criteria for Univalent functions, Proc. Amer. Math. Soc. 49 (1975), 109-115.
[27] S. Ruscheweyh, T. Shiel-Small, Hadamard product of schlicht functions and the Polya-Schoenberg Conjecture, Commen. Math. Helv. 48 (1973), 119-135.
[28] G. S. Salagean, Subclasses of Univalent functions, Lectur e Notes in Math. Springer Verlag, Berlin, 1013 (1983), 362-372.
[29] H. M. Srivastava, N-Eng Xu, Diang-Gong Yang, Inclusion relations and convolution properties of a certain class of analytic functions associated with Ruscheweyh derivatives, J. Math. Anal. Appl. 331 (2007), 686-700.

Citation :

Vinod Kumar, Prachi Srivastava, "Inclusion Attributes with Applications for Certain Subclasses of Analytic Subroutines," International Journal of Mathematics Trends and Technology (IJMTT), vol. 37, no. 1, pp. 55-66, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V37P508