On Variability Regions and Coefficient Inequalities for Exponentially Convex Janowski Functions

The current study concerns explicitly obtaining regions of variability described as \(Rρ[α,A,B;z_0]:=\{log f'(z_0)+α f(z_0):fρ[α,A,B]\}\) for the subclass \(E[α,A,B]\) of \(α\)-exponentially convex Janowski analytic functions. Also, sharp initial coefficient bounds are obtained, and the corresponding Fekete-Szegö functional is solved to answer a recently posed open problem partially. The work presented herein generalizes and unifies various known results reported earlier. Geometric illustrations for various involved parameters support the current findings.