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

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Published/Copyright: May 23, 2020
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 70 Issue 3

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)n−1(2n−1)(n−1)!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.

Keywords: 𝔮-starlike error function; 𝔮-convex error function; subordination; convolution
MSC 2010: Primary 30C45; 30C50; Secondary 05A30

  1. Communicated by Stanis lawa Kanas

References

[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.Search in Google Scholar

[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), 555–572.10.18514/MMN.2017.2207Search in Google Scholar

[3] Aydoŭan, M.—Kahramaner, Y.—Polatoŭlu, Y. : Close-to-convex functions defined by fractional operator, Appl. Math. Sci. 7 (2013), 2769–2775.10.12988/ams.2013.13246Search in Google Scholar

[4] Jackson, F. H. : On 𝔮-functions and a certain difference operator, Transactions of the Royal Society of Edinburgh 46 (1908), 253–281.10.1017/S0080456800002751Search in Google Scholar

[5] Kanas, S.—Raducanu, D. : Some class of analytic functions related to conic domains, Math. Slovaca 64 (2014), 1183–1196.10.2478/s12175-014-0268-9Search in Google Scholar

[6] Kanas, S.—Tatarczak, A. : Constrained coefficients problem for generalized typically real functions, Complex Var. Elliptic Equ. 61 (2016), 1052–1063.10.1080/17476933.2015.1135551Search in Google Scholar

[7] Kanas, S.—Tatarczak, A. : Generalized typically real functions, Filomat 30 (2016), 1697–1710.10.2298/FIL1607697KSearch in Google Scholar

[8] Naraniecka, I.—Szynal, J.—Tatarczak, A. : An extension of typically-real functions and associated orthogonal polynomials, Ann. UMCS Mathematica 65 (2011), 99–112.10.2478/v10062-011-0017-2Search in Google Scholar

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

[10] Ramachandran, C.—Vanitha, L. S.—Kanas, S. : Certain results on 𝔮-starlike and 𝔮-convex error functions, Math. Slovaca 68 (2018), 361–368.10.1515/ms-2017-0107Search in Google Scholar

[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.Search in Google Scholar

[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), 503–516.10.2298/FIL1802503SSearch in Google Scholar

[13] Tatarczak, A. : An extension of the Chebyshev polynomials, Complex Anal. Oper. Theory 10 (2016), 1519–1533.10.1007/s11785-015-0503-6Search in Google Scholar

Received: 2019-01-17
Accepted: 2019-05-13
Published Online: 2020-05-23
Published in Print: 2020-06-25

© 2020 Mathematical Institute Slovak Academy of Sciences

Articles in the same Issue

  1. Regular papers
  2. Recurrences for the genus polynomials of linear sequences of graphs
  3. The existence of states on EQ-algebras
  4. On sidon sequences of farey sequences, square roots and reciprocals
  5. Repdigits as sums of three balancing numbers
  6. Lipschitz one sets modulo sets of measure zero
  7. Refinement of fejér inequality for convex and co-ordinated convex functions
  8. An extension of q-starlike and q-convex error functions endowed with the trigonometric polynomials
  9. Coefficients problems for families of holomorphic functions related to hyperbola
  10. Triebel-Lizorkin capacity and hausdorff measure in metric spaces
  11. The method of upper and lower solutions for integral boundary value problem of semilinear fractional differential equations with non-instantaneous impulses
  12. On a system of three difference equations of higher order solved in terms of Lucas and Fibonacci numbers
  13. Density of summable subsequences of a sequence and its applications
  14. Rough weighted 𝓘-limit points and weighted 𝓘-cluster points in θ-metric space
  15. A note on cosine series with coefficients of generalized bounded variation
  16. Some geometric properties of the non-Newtonian sequence spaces lp(N)
  17. On sequence spaces defined by the domain of a regular tribonacci matrix
  18. Jointly separating maps between vector-valued function spaces
  19. Some fixed point theorems for multi-valued mappings in graphical metric spaces
  20. Monotone transformations on the cone of all positive semidefinite real matrices
  21. Locally defined operators in the space of Ck,ω-functions
  22. Some properties of D-weak operator topology
  23. Estimating the distribution of a stochastic sum of IID random variables
  24. An internal characterization of complete regularity
https://doi.org/10.1515/ms-2017-0374
Keywords for this article
𝔮-starlike error function; 𝔮-convex error function; subordination; convolution

Articles in the same Issue

  1. Regular papers
  2. Recurrences for the genus polynomials of linear sequences of graphs
  3. The existence of states on EQ-algebras
  4. On sidon sequences of farey sequences, square roots and reciprocals
  5. Repdigits as sums of three balancing numbers
  6. Lipschitz one sets modulo sets of measure zero
  7. Refinement of fejér inequality for convex and co-ordinated convex functions
  8. An extension of q-starlike and q-convex error functions endowed with the trigonometric polynomials
  9. Coefficients problems for families of holomorphic functions related to hyperbola
  10. Triebel-Lizorkin capacity and hausdorff measure in metric spaces
  11. The method of upper and lower solutions for integral boundary value problem of semilinear fractional differential equations with non-instantaneous impulses
  12. On a system of three difference equations of higher order solved in terms of Lucas and Fibonacci numbers
  13. Density of summable subsequences of a sequence and its applications
  14. Rough weighted 𝓘-limit points and weighted 𝓘-cluster points in θ-metric space
  15. A note on cosine series with coefficients of generalized bounded variation
  16. Some geometric properties of the non-Newtonian sequence spaces lp(N)
  17. On sequence spaces defined by the domain of a regular tribonacci matrix
  18. Jointly separating maps between vector-valued function spaces
  19. Some fixed point theorems for multi-valued mappings in graphical metric spaces
  20. Monotone transformations on the cone of all positive semidefinite real matrices
  21. Locally defined operators in the space of Ck,ω-functions
  22. Some properties of D-weak operator topology
  23. Estimating the distribution of a stochastic sum of IID random variables
  24. An internal characterization of complete regularity
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