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On q-analogue of Janowski-type starlike functions with respect to symmetric points

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Języki publikacji
EN
Abstrakty
EN
The main objective of the present paper is to define a class of q-starlike functions with respect to symmetric points in circular domain. Some interesting results of these functions have been evaluated in this article. The sufficiency criteria in the form of convolutions are evaluated. Furthermore, other geometric properties such as coefficient bounds, distortion theorem, closure theorem and extreme point theorem are also obtained for these newly defined functions.
Wydawca
Rocznik
Strony
37--46
Opis fizyczny
Bibliogr. 23 poz.
Twórcy
  • Institute of Numerical Sciences, Kohat University of Science and Technology, Kohat, Pakistan
  • Govt. Degree College Mardan, 23200, Mardan, Pakistan
autor
  • Department of Mathematics, FATA University TSD Darra Adam Khel, NMD Kohat, Pakistan
  • Institute of Numerical Sciences, Kohat University of Science and Technology, Kohat, Pakistan
  • Department of Mathematics, Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, 21030, Kuala Nerus, Terengganu, Malaysia
Bibliografia
  • [1] F. H. Jackson, On q-definite integrals, Quart. J. Pure. Appl. Math. 41(1910), 193–203.
  • [2] F. H. Jackson, On q-difference equations, Amer. J. Math. 32(1910), 305–314.
  • [3] M. E. Ismail, E. Merkes, and D. Styer, A generalization of starlike functions, Complex Var. Theory Appl. 14(1990), no. 1–4, 77–84.
  • [4] G. A. Anastassiou and S. G. Gal, Geometric and approximation properties of some singular integrals in the unit disk, J. Inequal. Appl. 2006(2006), 17231, DOI: https://doi.org/10.1155/JIA/2006/17231.
  • [5] G. A. Anastassiou and S. G. Gal, Geometric and approximation properties of generalized singular integrals in the unit disk, J. Korean Math. Soc. 43(2006), no. 2, 425–443, DOI: https://doi.org/10.4134/JKMS.2006.43.2.425.
  • [6] H. M. Srivastava, Univalent functions, fractional calculus, and associated generalized hypergeometric functions, in: H. M. Srivastava, S. Owa (eds.), Univalent Functions, Fractional Calculus, and Their Applications, Halsted Press, Ellis Horwood Limited, Chichester; John Wiley and Sons: New York, NY, USA; Chichester, UK; Brisbane, Australia; Toronto, ON, Canada, 1989; pp. 329–354.
  • [7] H. M. Srivastava, Some generalizations and basic (or q-) extentions of the Bernoulli, Euler and Genocchi polynomials, Appl. Math. Inform. Sci. 5(2011), no. 3, 390–444.
  • [8] A. Aral and V. Gupta, On q-Baskakov type operators, Demonstr. Math. 42(2009), 109–122.
  • [9] A. Aral and V. Gupta, On the Durrmeyer type modification of the q-Baskakov type operators, Nonlinear Anal. 72(2010), no. 3–4, 1171–1180.
  • [10] A. Aral and V. Gupta, Generalized q-Baskakov operators, Math. Slovaca 61(2011), 619–634.
  • [11] H. Aldweby and M. Darus, On harmonic meromorphic functions associated with basic hypergeometric functions, Sci. World J. 2013(2013), 164287, DOI: https://doi.org/10.1155/2013/164287.
  • [12] H. Aldweby and M. Darus, A subclass of harmonic univalent functions associated with q-analogue of Dziok-Srivastava operator, ISRN Mathematical Analysis 2013(2013), 382312, DOI: https://doi.org/10.1155/2013/382312.
  • [13] H. M. Srivastava, Operators of basic(or q-) calculus and fractional q-calculus and their applications in geometric function theory of complex analysis, Iran. J. Sci. Technol. Trans. A Sci. 44(2020), 327–344, DOI: https://doi.org/10.1007/s40995-019-00815-0.
  • [14] B. Khan, Z. G. Liu, H. M. Srivastava, N. Khan, M. Darus, and M. Tahir, A study of some families of multivalent q-starlike functions involving higher order q-derivatives, Mathematics 8(2020), no. 9, 1470, DOI: https://doi.org/10.3390/math8091470.
  • [15] L. Shi, M. G. Khan, and B. Ahmad, Some geometric properties of a family of analytic functions involving a generalized q-operator, Symmetry 12(2020), no. 2, 291, DOI: https://doi.org/10.3390/sym12020291.
  • [16] B. Khan, H. M. Srivastava, N. Khan, M. Darus, M. Tahir, and Q. Z. Ahmad, Coefficients estimates for a subclass of analytic functions associated with a certain leaf-like domain, Mathematics 8(2020), no. 8, 1334, DOI: https://doi.org/10.3390/math8081334.
  • [17] T. M. Seoudy and M. K. Aouf, Coefficient estimates of new classes of q-starlike and q-convex functions of complex order, J. Math. Inequal. 10(2016), 135–145, DOI: https://dx.doi.org/10.7153/jmi-10-11.
  • [18] B. Ahmad, M. G. Khan, B. A. Frasin, T. Abdeljawad, W. K. Mashwani, and M. Arif, On q-analogue of meromorhic multivalent functions in lemniscate of Bernouli domain, AIMS Math. 6(2021), no. 4, 3037–3052, DOI: https://doi.org/10.3934/math.2021185.
  • [19] S. Islam, M. G. Khan, B. Ahmad, M. Arif, and R. Chinram, Q-extension of starlike functions subordinated with a trigonometric sine function, Mathematics 8(2020), no. 10, 1676, DOI: https://doi.org/10.3390/math8101676.
  • [20] S. S. Miller and P. T. Mocanu, Differential subordination and univalent functions, Michigan Math. J. 28(1918), no. 2,157–171.
  • [21] S. S. Miller and P. T. Mocanu, Differential subordination: theory and applications, Series on Monographs and Textbooks in Pure and Applied Mathematics, no. 225; Marcel Dekker Incorporated, New York, NY, USA: Basel, Switzerland, 2000.
  • [22] K. Sakaguchi, On a certain univalent mapping, J. Math. Soc. Jpn. 2(1959), 72–75.
  • [23] W. Rogosinski, On the coefficients of subordinate functions, Proc. London Math. Soc. 48(1943), 48–82.
Uwagi
PL
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
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