An extension of q-starlike and q-convex error functions endowed with the trigonometric polynomials

  • 1 Department of Mathematics, Bursa Uludag University, 16059, Bursa, Turkey
Şahsene Altinkaya

Abstract

In this present investigation, we will concern with the family of normalized analytic error function which is defined by

Erf(z)=πz2erf(z)=z+n=2(1)n1(2n1)(n1)!zn.

By making the use of the trigonometric polynomials Un(p, q, eiθ) as well as the rule of subordination, we introduce several new classes that consist of 𝔮-starlike and 𝔮-convex error functions. Afterwards, we derive some coefficient inequalities for functions in these classes.

  • [1]

    Ali, R. M.—Lee, S. K.—Ravichandran, V.—Supramanian, S. : The Fekete-Szegö coefficient functional for transforms of analytic funtions, Bull. Iranian Math. Soc. 35 (2009), 119–142.

  • [2]

    Altinkaya, Ş.—Yalçin, S. : Faber polynomial coefficient estimates for bi-univalent functions of complex order based on subordinate conditions involving of the Jackson (p, q) -derivative operator, Miskolc Math. Notes 18 (2017), 555–572.

    • Crossref
    • Export Citation
  • [3]

    Aydoŭan, M.—Kahramaner, Y.—Polatoŭlu, Y. : Close-to-convex functions defined by fractional operator, Appl. Math. Sci. 7 (2013), 2769–2775.

  • [4]

    Jackson, F. H. : On 𝔮-functions and a certain difference operator, Transactions of the Royal Society of Edinburgh 46 (1908), 253–281.

  • [5]

    Kanas, S.—Raducanu, D. : Some class of analytic functions related to conic domains, Math. Slovaca 64 (2014), 1183–1196.

  • [6]

    Kanas, S.—Tatarczak, A. : Constrained coefficients problem for generalized typically real functions, Complex Var. Elliptic Equ. 61 (2016), 1052–1063.

    • Crossref
    • Export Citation
  • [7]

    Kanas, S.—Tatarczak, A. : Generalized typically real functions, Filomat 30 (2016), 1697–1710.

    • Crossref
    • Export Citation
  • [8]

    Naraniecka, I.—Szynal, J.—Tatarczak, A. : An extension of typically-real functions and associated orthogonal polynomials, Ann. UMCS Mathematica 65 (2011), 99–112.

  • [9]

    Purohit, S. D.—Raina, R. K. : Fractional 𝔮-calculus and certain subclass of univalent analytic functions, Mathematica 55 (2013) 62–74.

  • [10]

    Ramachandran, C.—Vanitha, L. S.—Kanas, S. : Certain results on 𝔮-starlike and 𝔮-convex error functions, Math. Slovaca 68 (2018), 361–368.

    • Crossref
    • Export Citation
  • [11]

    Srivastava, H. M. : Univalent Functions, Fractional Calculus, and Associated Generalized Hypergeometric Functions. In: Univalent Functions, Fractional Calculus, and Their Applications (H. M. Srivastava and S. Owa, eds.), Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1989.

  • [12]

    Srivastava, H. M.—Altinkaya, Ş.—Yalçin, S. : Hankel determinant for a subclass of Bi-univalent functions defined by using a symmetric 𝔮-derivative operator, Filomat 32 (2018), 503–516.

    • Crossref
    • Export Citation
  • [13]

    Tatarczak, A. : An extension of the Chebyshev polynomials, Complex Anal. Oper. Theory 10 (2016), 1519–1533.

    • Crossref
    • Export Citation
Purchase article
Get instant unlimited access to the article.
$42.00
Log in
Already have access? Please log in.


or
Log in with your institution

Journal + Issues

Mathematica Slovaca, the oldest and best mathematical journal in Slovakia, was founded in 1951 at the Mathematical Institute of the Slovak Academy of Science, Bratislava. It covers practically all mathematical areas. As a respectful international mathematical journal, it publishes only highly nontrivial original articles with complete proofs by assuring a high quality reviewing process.

Search