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A class of analytic functions associated with sine hyperbolic functions

  • S. Sivaprasad Kumar,
  • Muhammad Ghaffar Khan,
  • Bakhtiar Ahmad,
  • Wali Khan Mashwani

摘要

We introduce a class of analytic functions subordinated to \(1+\sinh \left( z\right)\) 1 + sinh z and obtain various necessary and sufficient conditions for functions to be in this class. These conditions mainly comprise of various results involving convolution. Further, we have obtained sharp five initial coefficients, a conjecture for the general nth coefficients and the third Hankel determinant bounds for the functions in this class. Also derived certain differential subordination implication results involving \(1+\sinh \left( z\right)\) 1 + sinh z .