Real fixed points and singular values of family of functions arising from generating function of unified generalized Apostol-type polynomials

Our main objective is to study the real fixed points and singular values of a two-parameter family of transcendental meromorphic functions g λ , n ( z ) = λ z/ ( b z − 1 ) n , λ ∈ R ∖ { 0 } , z ∈ C ∖ { 0 } , n ∈ N ∖ { 1 } , b 0 , b ≠ 1 in the present paper which obtains from generating function of the unified generalized Apostol-type polynomials. The real fixed points of g λ , n ( x ) , x ∈ R ∖ { 0 } with their stability are found for n odd and n even. It is shown that g λ , n ( z ) has infinite number of singular values. Further, it is seen that some critical values of g λ , n ( z ) lie in the closure of the disk and other lie in the exterior of the disk with center at the origin.