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Certain classes of analytic functions defined by Hurwitz-Lerch zeta function

Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this work, we introduce and investigate a new class k - ~USs (b, μ, γ, t) of analytic functions in the open unit disk U with negative coefficients. The object of the present paper is to determine coefficient estimates, neighborhoods and partial sums for functions f belonging to this class.
Wydawca
Rocznik
Strony
73--81
Opis fizyczny
Bibliogr. 21 poz.
Twórcy
  • Department of Mathematics, GSS, GITAM University, Doddaballapur-562 163, Bengaluru Rural, Karnataka, India
  • Department of Mathematics, Kakatiya University, Warangal-506 009, Telangana, India
autor
  • Department of Mathematics, GSS, GITAM University, Doddaballapur-562 163, Bengaluru Rural, Karnataka, India
  • Department of Mathematics, GSS, GITAM University, Doddaballapur-562 163, Bengaluru Rural, Karnataka, India
Bibliografia
  • [1] J. W. Alexander, Functions which map the interior of the unit circle upon simple regions, Ann. of Math. (2) 17 (1915), no. 1, 12-22.
  • [2] E. Aqlan, J. M. Jahangiri and S. R. Kulkarni, New classes of k-uniformly convex and starlike functions, Tamkang J. Math. 35 (2004), no. 3, 261-266.
  • [3] S. D. Bernardi, Convex and starlike univalent functions, Trans. Amer. Math. Soc. 135 (1969), 429-446.
  • [4] J. Choi and H. M. Srivastava, Certain families of series associated with the Hurwitz-Lerch zeta function, Appl. Math. Comput. 170 (2005), no. 1, 399-409.
  • [5] C. Ferreira and J. L. López, Asymptotic expansions of the Hurwitz-Lerch zeta function, J. Math. Anal. Appl. 298 (2004), no. 1, 210-224.
  • [6] T. M. Flett, The dual of an inequality of Hardy and Littlewood and some related inequalities, J. Math. Anal. Appl. 38 (1972), 746-765.
  • [7] M. Garg, K. Jain and H. M. Srivastava, Some relationships between the generalized Apostol-Bernoulli polynomials and Hurwitz-Lerch zeta functions, Integral Transforms Spec. Funct. 17 (2006), no. 11, 803-815.
  • [8] A. W. Goodman, Univalent functions and nonanalytic curves, Proc. Amer. Math. Soc. 8 (1957), 598-601.
  • [9] A. W. Goodman, On uniformly starlike functions, J. Math. Anal. Appl. 155 (1991), no. 2, 364-370.
  • [10] I. B. Jung, Y. C. Kim and H. M. Srivastava, The Hardy space of analytic functions associated with certain one-parameter families of integral operators, J. Math. Anal. Appl. 176 (1993), no. 1, 138-147.
  • [11] S.-D. Lin and H. M. Srivastava, Some families of the Hurwitz-Lerch zeta functions and associated fractional derivative and other integral representations, Appl. Math. Comput. 154 (2004), no. 3, 725-733.
  • [12] S.-D. Lin, H. M. Srivastava and P.-Y. Wang, Some expansion formulas for a class of generalized Hurwitz-Lerch zeta functions, Integral Transforms Spec. Funct. 17 (2006), no. 11, 817-827.
  • [13] S. Owa, T. Sekine and R. Yamakawa, On Sakaguchi type functions, Appl. Math. Comput. 187 (2007), no. 1, 356-361.
  • [14] J. K. Prajapat and S. P. Goyal, Applications of Srivastava-Attiya operator to the classes of strongly starlike and strongly convex functions, J. Math. Inequal. 3 (2009), no. 1, 129-137.
  • [15] D. Răducanu and H. M. Srivastava, A new class of analytic functions defined by means of a convolution operator involving the Hurwitz-Lerch zeta function, Integral Transforms Spec. Funct. 18 (2007), no. 11-12, 933-943.
  • [16] S. Ruscheweyh, Neighborhoods of univalent functions, Proc. Amer. Math. Soc. 81 (1981), no. 4, 521-527.
  • [17] K. Sakaguchi, On a certain univalent mapping, J. Math. Soc. Japan 11 (1959), 72-75.
  • [18] M. P. Santosh, R. N. Ingle, P. Thirupathi Reddy and B. Venkateswarlu, A new subclass of analytic functions defined by linear operator, Adv. in Math. Sci. J. 9 (2010), 205-217.
  • [19] H. Silverman, Partial sums of starlike and convex functions, J. Math. Anal. Appl. 209 (1997), no. 1, 221-227.
  • [20] E. M. Silvia, On partial sums of convex functions of order α, Houston J. Math. 11 (1985), no. 3, 397-404.
  • [21] H. M. Srivastava and A. A. Attiya, An integral operator associated with the Hurwitz-Lerch zeta function and differential subordination, Integral Transforms Spec. Funct. 18 (2007), no. 3-4, 207-216.
Uwagi
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).
Typ dokumentu
Bibliografia
Identyfikator YADDA
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