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Some Subclasses of Univalent and Bi-Univalent Functions Related to K-Fibonacci Numbers and Modified Sigmoid Function


  • Amal Madhi Rashid Department of Mathematics, College of Education for Pure Sciences, University of Anbar, Ramadi, Iraq.
  • Abdul Rahman S. Juma Department of Mathematics, College of Education for Pure Sciences, University of Anbar, Ramadi, Iraq.



Bi-univalent function, Borel distribution, Fibonacci numbers, Modified sigmoid function, Univalent function


            This paper is interested in certain  subclasses of univalent and bi-univalent functions concerning  to shell- like curves connected with k-Fibonacci numbers involving modified Sigmoid activation function θ(t)=2/(1+e^(-t) ) ,t ≥0 in unit disk |z|<1 . For estimating of the initial coefficients |c_2 | , |c_3 |, Fekete-Szego ̈ inequality and the  second Hankel determinant have been investigated for the functions in our classes. 


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