(untitled) (European Journal of Pure and Applied Mathematics, 2025)
This paper examines necessary and sufficient conditions for the function vs (z), Λ(s, v, z)B using coefficients of Touchard polynomials to be in the classes Q(δ, ζ) and K(δ, ζ) of analytic functions. Furthermore, we estimate certain inclusion relations between the classes Rτ (A1,A2) and K(δ, ζ). Finally, we give a necessary and sufficient condition for an integral operator J vs (z) to be in the class K(δ, ζ). Special cases for the classes of starlike and convex functions is also considered.