Banach spaces, as complete normed vector spaces, provide a fundamental setting in modern analysis, allowing for a rigorous treatment of convergence and stability in infinite dimensions. Integrability ...

For a fixed nonnegative integer m, an analytic map φ and an analytic function ψ the generalized integration operator I φ , ψ m is defined by I φ , ψ m f z = ∫ 0 z f m φ ζ ψ ζ d ζ for X-valued analytic ...

If the space of all real-valued functions of bounded variation on a real closed interval is endowed with the topology of simple convergence, then every bounded subset which is bounded for the values ...