Research article

New subclass of q-starlike functions associated with generalized conic domain

  • Received: 27 February 2020 Accepted: 20 May 2020 Published: 02 June 2020
  • MSC : 30C45, 30C50

  • In this paper, the concepts of quantum (or q-) calculus and conic regions are combined to define a new domain Ωk, q, γ which represents the generalized conic regions. Then by using a certain generalized conic domain Ωk, q, γ we define and investigate a new subclass of normalized analytic functions in open unit disk E. We also investigate a number of useful properties and characteristics of this subclass such as, structural formula, necessary and sufficient condition, coefficient estimates, Feketo-Szego problem, distortion inequalities, closure theorem, and subordination result. We also highlight some known consequences of our main results as corollaries.

    Citation: Xiaoli Zhang, Shahid Khan, Saqib Hussain, Huo Tang, Zahid Shareef. New subclass of q-starlike functions associated with generalized conic domain[J]. AIMS Mathematics, 2020, 5(5): 4830-4848. doi: 10.3934/math.2020308

    Related Papers:

  • In this paper, the concepts of quantum (or q-) calculus and conic regions are combined to define a new domain Ωk, q, γ which represents the generalized conic regions. Then by using a certain generalized conic domain Ωk, q, γ we define and investigate a new subclass of normalized analytic functions in open unit disk E. We also investigate a number of useful properties and characteristics of this subclass such as, structural formula, necessary and sufficient condition, coefficient estimates, Feketo-Szego problem, distortion inequalities, closure theorem, and subordination result. We also highlight some known consequences of our main results as corollaries.


    加载中


    [1] A. W. Goodman, Univalent Functions, vols. I, II. Polygonal Publishing House, New Jersey 1983.
    [2] A. W. Goodman, On uniformly convex functions, Ann. Polon. Math., 56 (1991), 87-92. doi: 10.4064/ap-56-1-87-92
    [3] W. Ma, D. Minda, Uniformly convex functions, Ann. Polon. Math., 57 (1992), 165-175. doi: 10.4064/ap-57-2-165-175
    [4] S. Kanas, A. Wisniowska, Conic domains and k-starlike functions, Rev. Roum. Math. Pure Appl., 45 (2000), 647-657.
    [5] F. Rønning, Uniformly convex functions and a corresponding class of starlike functions, Proc. Am. Math. Soc., 118 (1993), 189-196. doi: 10.1090/S0002-9939-1993-1128729-7
    [6] K. G. Subramanian, G. Murugusundaramoorthy, P. Balasubrahmanyam, et al. Subclasses of uniformly convex and uniformly starlike functions, Math. Jpn., 42 (1995), 517-522.
    [7] S. Kanas, A. Wisniowska, Conic regions and k-uniform convexity, J. Comput. Appl. Math., 105 (1999), 327-336. doi: 10.1016/S0377-0427(99)00018-7
    [8] E. Deniz, M. Caglar, H. Orhan, The Fekete-Szego problem for a class of analytic functions defined by Dziok-Srivastava operator, Kodai Math. J., 35 (2012), 439-462. doi: 10.2996/kmj/1352985448
    [9] E. Deniz, H. Orhan, J. Sokol, Classes of analytic functions defined by a differential operator related to conic domains, Ukr. Math. J., 67 (2016), 1367-1385. doi: 10.1007/s11253-016-1159-8
    [10] S. Shams, S. R. Kulkarni, J. M. Jahangiri, Classes of uniformly starlike and convex functions, Int. J. Math. Math. Sci., 55, (2004), 2959-2961.
    [11] H. M. Srivastava, Univalent functions, fractional calculus, and associated generalized hypergeometric functions, In: H. M. Srivastava, S. Owa, Univalent functions, fractional Calculus, and Their Applications, John Wiley Sons, New York, etc. 1989.
    [12] F. H. Jackson, On q-functions and a certain difference operator, Transactions of the Royal Society of Edinburgh, 46 (1908), 253-281.
    [13] A. Aral, V. Gupta, On q-Baskakov type operators, Demon-stratio Math., 42, (2009), 109-122.
    [14] A. Aral, On the generalized Picard and Gauss Weierstrass singular integrals, J. Comput. Anal. Appl., 8 (2006), 249-261.
    [15] S. Kanas, D. Raducanu, Some class of analytic functions related to conic domains, Math. Slovaca, 64 (2014), 1183-1196.
    [16] M. Arif, H. M. Srivastava, S. Uma, Some applications of a q-analogue of the Ruscheweyh type operator for multivalent functions, RACSAM, 113 (2019), 1211-1221. doi: 10.1007/s13398-018-0539-3
    [17] M. Arif, Z. G. Wang, R. Khan, et al. Coefficient inequalities for Janowski-Sakaguchi type functions associated with conic regions, Hacet. J. Math. Stat., 47 (2018), 261-271.
    [18] L. Shi, M. Raza, K. Javed, et al. Class of analytic functions defined by q-integral operator in a symmetric region, Symmetry, 11 (2019), 1042.
    [19] H. M. Srivastava, S. Khan, Q. Z. Ahmad, et al. The Faber polynomial expansion method and its application to the general coefficient problem for some subclasses of bi-univalent functions associated with a certain q-integral operator, Stud. Univ. Babe s-Bolyai Math., 63 (2018), 419-436. doi: 10.24193/subbmath.2018.4.01
    [20] G. Gasper, M. Rahman, Basic Hpergeometric series, vol. 35 of Encyclopedia of Mathematics and its applications, Ellis Horwood, Chichester, UK, 1990.
    [21] M. E. H. Ismail, E. Merkes, D. Styer, A generalization of starlike functions, Complex Var. Theory Appl., 14 (1990), 77-84.
    [22] H. E. O. Uçar, Coefficient inequality for q-starlike Functions, Appl. Math. Comput., 76 (2016), 122-126.
    [23] W. Rogosinski, On the coefficients of subordinate functions, Proc. Lond. Math. Soc., 48 (1943), 48-82.
    [24] Y. J. Sim, O. S. Kwon, N. E. Cho, et al. Some classes of analytic functions associated with conic regions, Taiwan J. Math., 16 (2012), 387-408. doi: 10.11650/twjm/1500406547
    [25] 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.
    [26] W. Ma, D. Minda, A unified treatment of some special classes of univalent functions. In: Z. Li, F. Ren, L. Yang, et al. (Eds.) Proceedings of the Conferene on Complex Analysis, Int. Press Inc. (1992), 157-169.
  • Reader Comments
  • © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(4074) PDF downloads(385) Cited by(16)

Article outline

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog