Application of Convolution Theory on Non-Linear Integral Operators

Abstract

The class W δ β (α, γ) defined in the domain |z| < 1 satisfyingwith the conditions α ≥ 0, β < 1, γ ≥ 0, δ > 0 and φ ∈ R generalizes a particular case of the largest subclass of univalent functions, namely the class of Bazilevič functions. Moreover, for 0In the present work, the sufficient conditions on λ(t) are investigated, so that the non-linear integral transform. Several interesting applications are provided for special choices of λ(t). These results are useful in the attempt to generalize the two most important extremal problems in this direction using duality techniques and provide scope for further research.