Abstract
The singular values of two kinds of two-parameter families of functions (i) f(lambda,mu)(z) = A((b(z) - 1)/z)(mu) and f(lambda,mu)(0)= lambda(ln b)(mu), mu > 0, (ii) g(lambda,eta)(z) = lambda(z/(b(z) - 1))(eta) and g(lambda,eta)(0)=A/On br, i>0; 2 E R\{0}, z E C, b > 0, b 1 are described. It is shown that all the critical values f(lambda,mu)(z) and gx,(z) lie interior and exterior of the disk centered at origin and having radii vertical bar lambda(ln - b)(mu) and vertical bar lambda/(ln b)(eta)vertical bar respectively. Further, it is proved that both the functionsfk,(z) and gx,n(z) have infinitely many singular values for all b > 0, b not equal 1. (C) 2016 The Author. Production and hosting by Elsevier B.V. on behalf of Taibah University.