Acta mathematica scientia, Series B >
ON A CLASS OF ANALYTIC FUNCTIONS RELATED TO CONIC DOMAINS AND ASSOCIATED WITH CARLSON-SHAFFER OPERATOR
Received date: 2010-12-10
Revised date: 2011-10-26
Online published: 2012-07-20
Making use of the Carlson–Shaffer convolution operator, we introduce and study a new class of analytic functions related to conic domains. The main object of this paper is to investigate inclusion relations, coefficient bound for this class. We also show that this class is closed under convolution with a convex function. Some applications are also discussed.
S. HUSSAIN , J. SOKóL . ON A CLASS OF ANALYTIC FUNCTIONS RELATED TO CONIC DOMAINS AND ASSOCIATED WITH CARLSON-SHAFFER OPERATOR[J]. Acta mathematica scientia, Series B, 2012 , 32(4) : 1399 -1407 . DOI: 10.1016/S0252-9602(12)60108-8
[1] Altinta¸s O, ÖzkanÖ. Applications of differential subordination. Appl Math Lett, 2006, 19: 728–734
[2] Al-Amiri H S, Fernando T S. On close-to-convex functions of complex order. Int J Math Sci, 1990, 13: 321–330
[3] Acu M. Some subclasses of -uniformly convex functions. Acta Mathematica Academiae Pedagogicae Nyiregyhaziensis 2005, 21: 49–54
[4] Bharati R, Parvatham R, Swaminathan A. On subclasses of uniformly convex functions and corresponding class of starlike functions. Tamkang J Math, 1997, 28(1): 17–32
[5] Carlson B C, Shaeffer D B. Starlike and pre-starlike hypergeometric functions. SIAM J Math Anal, 1984, 15: 737–745
[6] Gangadharan A, Shanmugam T N, Srivastava H M. Generalized hypergeometric functions associated with k-uniformly convex functions. Comput Math Appl, 2002, 44: 1515–1526
[7] Goodman A W. On uniformly convex functions. Ann Polon Math, 1991, 56(1): 87–92
[8] Kanas S, Srivastava H M. Linear operators associated with k-uniformly convex functions. Integral Trans-form Spec Funct, 2000, 9(2): 121–132
[9] Kanas S,Wi´sniowska A. Conic regions and k-uniform convexity. J Comput Appl Math, 1999, 105: 327–336
[10] Kanas S, Wi´sniowska A. Conic domains and k-starlike functions. Rev Roumaine Math Pures Appl, 2000, 45(4): 647–657
[11] Lecko A, Wi´sniowska A. Geometric properties of subclasses of starlike functions. J Comput Appl Math, 2003, 155: 383–387
[12] Ma W, Minda D. Uniformly convex functions. Ann Polon Math, 1992, 57(2): 165–175
[13] Mannino A. Some inequalities concerning starlike and convex functions. Gen Math, 2004, 12(1): 5–12
[14] Miller S S, Mocanu P T. Differential subordination and univalent functions. Michigan Math J, 1981, 28: 157–171
[15] Miller S S, Mocanu P T. Differential Subordinations: Theory and Applications. Series of Monographs and Textbooks in Pure and Applied Mathematics, Vol 225. New York/Basel: Marcel Dekker Inc, 2000
[16] Subramanian K G, Murugusundaramoorthy G, Balasubrahmanyam P, Silverman H. Subclasses of uni-formly convex and uniformly starlike functions. Math Japon, 1995, 42(3): 517–522
[17] Noor K I, Arif M, Ul-Haq W. On k-uniformly close-to-convex functions of complex order. Appl Math Comput, 2009, 215: 629–635
[18] Rønning F. Uniformly convex functions and a corresponding class of starlike functions. Proc Amer Math Soc, 1993, 118: 189–196
[19] Ruscheweyh S. Convolution in Geometric Function Theory. Sem Math Sup, Vol 83. Montreal: Presses Univ Montreal, 1982
[20] Ruscheweyh St. New criteria for univalent functions. Proc Amer Math Soc, 1975, 49: 109–115
[21] Swaminathan A. Hypergeometric functions in the parabolic domain. Tamsui Oxf J Math Sci, 2004, 20(1): 1–16
[22] Trojnar-Spelina L. On certain applications of the Hadamard product. Appl Math Comput, 2008, 199: 653–662
[23] Wi´sniowska-Wajnryb A. Some extremal bounds for subclass of univalent functions. Appl Math Comput, 2009, 215: 2634–2641
/
| 〈 |
|
〉 |