NEW SUBCLASS OF ANALYTIC FUNCTIONS IN CONICAL DOMAIN ASSOCIATED WITH A LINEAR OPERATOR

doi:10.1016/S0252-9602(16)30033-9

数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (3): 704-716.doi: 10.1016/S0252-9602(16)30033-9

NEW SUBCLASS OF ANALYTIC FUNCTIONS IN CONICAL DOMAIN ASSOCIATED WITH A LINEAR OPERATOR

Muhammed ARIF¹, Shahid MAHMOOD¹, Janusz SOKÓ?², Jacek DZIOK³

1. Department of Mathematics, Abdulwali Khan University Mardan, Pakistan;
2. Department of Mathematics, Rzeszów University of Technology, Al. Powstańców Warszawy 12, 35-959 Rzeszów, Poland;
3. Institute of Mathematics, University of Rzeszów, ul. Rejtana 16 A, 35-310 Rzeszów, Poland

收稿日期:2015-04-03 出版日期:2016-06-25 发布日期:2016-06-25
通讯作者: Janusz SOKÓŁ,E-mail:jsokol@prz.edu.pl E-mail:jsokol@prz.edu.pl
作者简介:Muhammed ARIF,E-mail:marifmaths@yahoo.com;Shahid MAHMOOD,E-mail:shahidmahmood757@gmail.com;Jacek DZIOK,E-mail:jdziok@univ.rzeszow.pl

NEW SUBCLASS OF ANALYTIC FUNCTIONS IN CONICAL DOMAIN ASSOCIATED WITH A LINEAR OPERATOR

Muhammed ARIF¹, Shahid MAHMOOD¹, Janusz SOKÓ?², Jacek DZIOK³

1. Department of Mathematics, Abdulwali Khan University Mardan, Pakistan;
2. Department of Mathematics, Rzeszów University of Technology, Al. Powstańców Warszawy 12, 35-959 Rzeszów, Poland;
3. Institute of Mathematics, University of Rzeszów, ul. Rejtana 16 A, 35-310 Rzeszów, Poland

Received:2015-04-03 Online:2016-06-25 Published:2016-06-25
Contact: Janusz SOKÓŁ,E-mail:jsokol@prz.edu.pl E-mail:jsokol@prz.edu.pl

摘要/Abstract

摘要：

The main object of the present paper is to investigate a number of useful properties such as inclusion relations, distortion bounds, coefficient estimates, subordination results, the Fekete-Szegö problem and some other for a new subclass of analytic functions, which are defined here by means of linear operator. Relevant connections of the results presented here with those obtained in earlier works are also pointed out.

关键词: analytic functions, subordination, functions with positive real part, linear operators, conic domains

Abstract:

Key words: analytic functions, subordination, functions with positive real part, linear operators, conic domains

中图分类号:

30C45

Muhammed ARIF, Shahid MAHMOOD, Janusz SOKÓŁ, Jacek DZIOK. NEW SUBCLASS OF ANALYTIC FUNCTIONS IN CONICAL DOMAIN ASSOCIATED WITH A LINEAR OPERATOR[J]. 数学物理学报(英文版), 2016, 36(3): 704-716.

Muhammed ARIF, Shahid MAHMOOD, Janusz SOKÓŁ, Jacek DZIOK. NEW SUBCLASS OF ANALYTIC FUNCTIONS IN CONICAL DOMAIN ASSOCIATED WITH A LINEAR OPERATOR[J]. Acta mathematica scientia,Series B, 2016, 36(3): 704-716.

参考文献

[1] Goodman A W. Univalent Functions, Vol I, II. Washington, New Jersey: Polygonal Publishing House, 1983
[2] Goodman A W. On uniformly convex functions. Ann Polon Math, 1991, 56(1): 87-92
[3] Ma W, Minda D. Uniformly convex functions. Ann Polon Math, 1992, 57(2): 165-175
[4] Rønning F. Uniformly convex functions and a corresponding class of starlike functions. Proc Amer Math Soc, 1993, 118: 189-196
[5] Kanas S, Wi?niowska A. Conic regions and k-uniform convexity. J Comput Appl Math, 1999, 105: 327-336
[6] Kanas S, Wi?niowska A. Conic domains and k-starlike functions. Rev Roumaine Math Pure Appl, 2000, 45: 647-657
[7] Subramanian K G, Murugusundaramoorthy G, Balasubrahmanyam P, Silverman H. Subclasses of uniformly convex and uniformly starlike functions. Math Japon, 1995, 42(3): 517-522
[8] 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
[9] Al-Amiri H S, Fernando T S. On close-to-convex functions of complex order. Int J Math Math Sci, 1990, 13: 321-330
[10] Acu M. Some subclasses of α-uniformly convex functions. Acta Mathematica Academiae Pedagogicae Nyir-egyhaziensis, 2005, 21: 49-54
[11] Gangadharan A, Shanmugam T N, Srivastava H M. Generalized hypergeometric functions associated with k-uniformly convex functions. Comput Math Appl, 2002, 44: 1515-1526
[12] Swaminathan S. Hypergeometric functions in the parabolic domain. Tamsui Oxf J Math Sci, 2004, 20(1): 1-16
[13] 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
[14] Carlson C S, Shaffer D B. Starlike and prestarlike hypergeometric functions. SIAM J Math Anal, 1984, 15: 737-745
[15] Ruscheweyh S. New criteria for univalent functions. Proc Amer Math Soc, 1975, 49: 109-115
[16] Hussain S, Sokó? J. On a Class of analytic functions related to conic domains and associated with Carlson-Shaffer operator. Acta Math Sci, 2012, 32B: 1-9
[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] Trojnar-Spelina L. On certain applications of the Hadamard product. Appl Math Comput, 2008, 199: 653-662
[19] Altinta? O, Özkan Ö. Applications of differential subordination. Appl Math Lett, 2006, 19: 728-734
[20] Sokó? J. On a class of analytic multivalent functions. Appl Math Comp, 2008, 203: 210-216
[21] Kanas S, Srivastava HM. Linear operators associated with k-uniformly convex functions. Integral Transform Spec Funct, 2000, 9(2): 121-132
[22] Lecko A, Wi?niowska A. Geometric properties of subclasses of starlike functions. J Comput Appl Math, 2003, 155: 383-387
[23] Mannino A. Some inequalities concerning starlike and convex functions. Gen Math, 200412(1): 5-12
[24] Wi?niowska-Wajnryb A. Some extremal bounds for subclass of univalent functions. Appl Math Comput, 2009, 215: 2634-2641
[25] Shams S, Kulkarni S R, Jahangiri J M. Classes of uniformly starlike and convex functions. Int J Math Math Sci, 2004, 55: 2959-2961
[26] Latha S. Coefficient inequalities for certain classes of Ruscheweyh type analytic functions. J. Ineq Pure Appl Maths, 2008, 9(2): 1-5
[27] Owa S, Polatoglu Y, Yavuz E. Coefficient inequalities for classes of uniformly starlike and convex functions. J Ineq Pure Appl Math, 2006, 7(5): 1-5
[28] Ali R M. Starlikeness associated with parabolic regions. Int J Math Math Sci, 2005, 4: 561-570
[29] Rogosinski W. On the coefficients of subordinate functions. Proc Lodon Math Soc, 1943, 48: 48-82
[30] Sim Y J, Kwon O S, Cho N E, Srivastava H M. Some classes of analytic functions associated with conic regions. Taiwanese J Math, 2012, 16(1): 387-408
[31] Ma M, Minda D. A unified treatment of some special classes of univalent functions//Li Z, Ren F, Yang L, Zhang S, eds. Proceedings of the Conference on Complex Analysis. International Press Inc, 1992: 157-169
[32] Sokó? J. Classes of analytic functions associated with the Choi-Saigo-Srivastava operator. J Math Anal Appl, 2006, 318: 517-525
[33] Arif M, Sokó? J, Ayaz M. Coefficient inequalities for a subclass of p-valent analytic functions. Sci World J, 2014, 2014: 1-5

NEW SUBCLASS OF ANALYTIC FUNCTIONS IN CONICAL DOMAIN ASSOCIATED WITH A LINEAR OPERATOR

NEW SUBCLASS OF ANALYTIC FUNCTIONS IN CONICAL DOMAIN ASSOCIATED WITH A LINEAR OPERATOR

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