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A subclass of uniformly convex functions and a corresponding subclass of starlike function with fixed coefficient associated with q-analogue of Ruscheweyh operator

  • Shahid Khan EMAIL logo , Saqib Hussain , Muhammad A. Zaighum and Maslina Darus
Published/Copyright: July 19, 2019
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 69 Issue 4

Abstract

Making use of Ruscheweyh q-differential operator, we define a new subclass of uniformly convex functions and corresponding subclass of starlike functions with negative coefficients. The main object of this paper is to obtain, coefficient estimates, closure theorems and extreme point for the functions belonging to this new class. The results are generalized to families with fixed finitely many coefficients.

MSC 2010: Primary 30C45; 30C50
Keywords: univalent function; convex function; starlike function; uniformly convex function; uniformly starlike function; Ruscheweyh q-differential operator

  1. (Communicated by Stanisława Kanas)

Acknowledgement

The authors would like to thank the Editor and referees for their valuable comments which helped to improve the manuscript. The 4th author is supported by UKM grant: GUP-2017-064.

References

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Received: 2018-08-25
Accepted: 2018-12-19
Published Online: 2019-07-19
Published in Print: 2019-08-27

© 2019 Mathematical Institute Slovak Academy of Sciences

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  1. Regular papers
  2. On the finite embeddability property for quantum B-algebras
  3. A dual Ramsey theorem for finite ordered oriented graphs
  4. On EMV-Semirings
  5. A nonsymmetrical matrix and its factorizations
  6. On weakly 𝓗-permutable subgroups of finite groups
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  8. A geometrical version of Hardy-Rellich type inequalities
  9. On a Choquet-Stieltjes type integral on intervals
  10. Uniqueness of meromorphic functions sharing four small functions on annuli
  11. A subclass of uniformly convex functions and a corresponding subclass of starlike function with fixed coefficient associated with q-analogue of Ruscheweyh operator
  12. Functions of bounded variation related to domains bounded by conic sections
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  14. Oscillatory criteria for the second order linear ordinary differential equations
  15. When deviation happens between rough statistical convergence and rough weighted statistical convergence
  16. The retraction of certain banach right modules associated to a character
  17. On sequence spaces generated by binomial difference operator of fractional order
  18. Some refinements of young type inequality for positive linear map
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  20. The beta exponentiated Nadarajah-Haghighi distribution: theory, regression model and application
  21. Hilbert algebras with supremum generated by finite chains
https://doi.org/10.1515/ms-2017-0271
Keywords for this article
univalent function; convex function; starlike function; uniformly convex function; uniformly starlike function; Ruscheweyh q-differential operator

Articles in the same Issue

  1. Regular papers
  2. On the finite embeddability property for quantum B-algebras
  3. A dual Ramsey theorem for finite ordered oriented graphs
  4. On EMV-Semirings
  5. A nonsymmetrical matrix and its factorizations
  6. On weakly 𝓗-permutable subgroups of finite groups
  7. The left Riemann-Liouville fractional Hermite-Hadamard type inequalities for convex functions
  8. A geometrical version of Hardy-Rellich type inequalities
  9. On a Choquet-Stieltjes type integral on intervals
  10. Uniqueness of meromorphic functions sharing four small functions on annuli
  11. A subclass of uniformly convex functions and a corresponding subclass of starlike function with fixed coefficient associated with q-analogue of Ruscheweyh operator
  12. Functions of bounded variation related to domains bounded by conic sections
  13. Unified solution of Fekete-Szegö problem for subclasses of starlike mappings in several complex variables
  14. Oscillatory criteria for the second order linear ordinary differential equations
  15. When deviation happens between rough statistical convergence and rough weighted statistical convergence
  16. The retraction of certain banach right modules associated to a character
  17. On sequence spaces generated by binomial difference operator of fractional order
  18. Some refinements of young type inequality for positive linear map
  19. On the Gromov-Hausdorff limit of metric spaces
  20. The beta exponentiated Nadarajah-Haghighi distribution: theory, regression model and application
  21. Hilbert algebras with supremum generated by finite chains
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