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Advances in Algebra and Analysis pp 141–149Cite as

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A New Subclass of Uniformly Convex Functions Defined by Linear Operator

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Abstract

In this paper, we define a new subclass of uniformly convex functions with negative coefficients and obtain coefficient estimates, extreme points, closure and inclusion theorems, and the radii of starlikeness and convexity for the new subclass. Furthermore, results on partial sums are discussed.

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References

  1. Carlson, B. C., Shaffer, S. B.: Starlike and prestarlike hypergeometric functions. SIAM J. Math. Anal. 15, 737–745 (2002)

    Article  MathSciNet  Google Scholar 

  2. Goodman, A. W.: On uniformly convex functions. Ann. Polon. Math. 56, 87–92 (1991)

    Article  MathSciNet  Google Scholar 

  3. Goodman, A. W.: On uniformly starlike functions. J. Math. Anal. & Appl. 155, 364–370 (1991)

    Article  MathSciNet  Google Scholar 

  4. Murugusundaramoorthy, G., Magesh, N.: Linear operators associated with a subclass of uniformly convex functions. Internat. J. Pure Appl. Math. Sci. 4, 113–125 (2006)

    Google Scholar 

  5. Ronning, F.: Uniformly convex functions and a corresponding class of starlike functions. Proc. Am. Math. Soc. 1(18), 189–196 (1993)

    Article  MathSciNet  Google Scholar 

  6. Ronning, F.: Integral representations for bounded starlike functions. Annal. Polon. Math. 60 , 289–297 (1995)

    Article  MathSciNet  Google Scholar 

  7. Schild, A., Silverman, H.: Convolution of univalent functions with negative co-efficient. Ann. Univ. Marie Curie-Sklodowska Sect. A. 29, 99–107 (1975)

    MATH  Google Scholar 

  8. Silverman, H.: Univalent functions with negative coefficients. Proc. Amer. Math. Soc. 51, 109–116 (1975)

    Article  MathSciNet  Google Scholar 

  9. Silverman, H.: Partial sums of starlike and convex functions. J. Math. Anal. & Appl. 209, 221–227 (1997)

    Article  MathSciNet  Google Scholar 

  10. Silvia, E. M.: Partial sums of convex functions of order α. Houston J. Math. 11, 517–522 (1985)

    Google Scholar 

  11. Subramanian, K. G., Murugusundaramoorthy, G., Balasubrahmanyam, P., Silverman, H.: Sublcasses of uniformly convex and uniformly starlike functions. Math Japonica. 42, 517–522 (1995)

    MathSciNet  MATH  Google Scholar 

  12. Subramanian, K. G., Sudharsan, T.V., Balasubrahmanyam, P., Silverman, H.: Classes of uniformly starlike functions. Publ. Math. Debrecen. 53, 309–315 (1998)

    MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Government A. V. V. College, Warangal, Telangana, India

    A. Narasimha Murthy

  2. Department of Mathematics, Kakatiya Univeristy, Warangal, Telangana, India

    P. Thirupathi Reddy

  3. Department of Mathematics, School of Advanced Sciences, VIT University, Vellore, Tamil Nadu, India

    H. Niranjan

Authors
  1. A. Narasimha Murthy
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  2. P. Thirupathi Reddy
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  3. H. Niranjan
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Corresponding author

Correspondence to H. Niranjan .

Editor information

Editors and Affiliations

  1. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India

    V. Madhu

  2. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India

    A. Manimaran

  3. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India

    D. Easwaramoorthy

  4. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India

    D. Kalpanapriya

  5. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India

    M. Mubashir Unnissa

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Murthy, A.N., Reddy, P.T., Niranjan, H. (2018). A New Subclass of Uniformly Convex Functions Defined by Linear Operator. In: Madhu, V., Manimaran, A., Easwaramoorthy, D., Kalpanapriya, D., Mubashir Unnissa, M. (eds) Advances in Algebra and Analysis. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-01120-8_17

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