Singular Values of One Parameter Family \(\lambda ((e^{z}-1)/z)^{m}\)

  • Authors

    2015-03-25
    https://doi.org/10.14419/ijamr.v4i2.4359
  • Critical values, Singular values

  • Abstract

    In the present paper, the singular values of one parameter family of entire functions \(f_{\lambda}(z)=\lambda\bigg(\dfrac{e^{z}-1}{z}\bigg)^{m}\) and \(f_{\lambda}(0)=\lambda\), \(m\in \mathbb{N}\backslash \{0\}\), \(\lambda\in \mathbb{R} \backslash \{0\}\), \(z \in \mathbb{C}\) is investigated. It is shown that all the critical values of \(f_{\lambda}(z)\) lie in the left half plane. It is also found that the function \(f_{\lambda}(z)\) has infinitely many bounded singular values and lie inside the open disk centered at origin and having radius \(|\lambda|\).

    Author Biography

    • Mohammad Sajid, Qassim University

      College of Engineering,

      Assistant Professor

  • References

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  • How to Cite

    Sajid, M. (2015). Singular Values of One Parameter Family \(\lambda ((e^{z}-1)/z)^{m}\). International Journal of Applied Mathematical Research, 4(2), 295-298. https://doi.org/10.14419/ijamr.v4i2.4359

    Received date: 2015-02-15

    Accepted date: 2015-03-09

    Published date: 2015-03-25