Let H(D) be the space of analytic functions on the unit disc and let (D) denote the set of analytic self-maps of D. Let Ψ = (ψj)j=0k be such that ψj ∈ H(D) and φ ∈ S(D). We characterize the boundedness, compactness and completely continuous of the sum of generalized weighted composition operators 'Equation Presented' between weighted Banach spaces of analytic functions Hv∞(Hv0) and Hw∞(Hw0) which unifies the study of products of composition operators, multiplication operators and differentiation operators. As applications, we obtain the boundedness and compactness of the generalized weighted composition operators Dψ,φn: v(ßv0) → w(ßw0), v(ßv0) → Hw∞(Hw0) and Hv∞(Hv0) → w(ßw0), where v(ßv0) and w(ßw0) are weighted Bloch-type (little Bloch-type) spaces. Also, new characterizations of the boundedness and compactness of the operators TΨ,φk and DΨ,φn are given. Examples of bounded, unbounded, compact and non-compact operators TΨ,φk and DΨ,φn are given to explain the role of inducing functions Ψj, φ and the weights v, w of the underlying weighted spaces.
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