Results on integration by parts and integration by substitution for the variational integral of Henstock are well-known. When real-valued functions are considered, such results also hold for the Generalized Riemann Integral defined by Kurzweil since, in this case, the integrals of Kurzweil and Henstock coincide. However, in a Banach-space valued context, the Kurzweil integral properly contains ...

‎We prove the existence of PPF dependent coincidence points for a pair of single-valued and multi-valued mappings satisfying generalized contractive conditions in Banach spaces‎. ‎Furthermore, the PPF dependent fixed point and PPF dependent common fixed point theorems for multi-valued mappings are proved.

Linear equivalences of norms of vector-valued singular integral operators and vector-valued martingale transforms are studied. In particular, it is shown that the UMD-constant of a Banach space X equals the norm of the real (or the imaginary) part of the BeurlingAhlfors singular integral operator, acting on LpX(R ) with p ∈ (1,∞). Moreover, replacing equality by a linear equivalence, this is fo...

where (n1,n2, . . . ,nd)= n∈ Z+. Recently, Thanh [11] proved (1.1) under condition of uniform integrability of {|Xn|p, n∈ Z+}. Mean convergence theorems for sums of random elements Banach-valued are studied by many authors. The reader may refer to Wei and Taylor [12], Adler et al. [2], Rosalsky and Sreehari [9], or more recently, Rosalsky et al. [10], Cabrera and Volodin [3]. However, we are un...

We obtain several Banach-Stone type theorems for vector-valued functions in this paper. Let X,Y be realcompact or metric spaces, E,F locally convex spaces, and φ a bijective linear map from C(X,E) onto C(Y, F ). If φ preserves zero set containments, i.e., z(f) ⊆ z(g)⇐⇒ z(φ(f)) ⊆ z(φ(g)), ∀ f, g ∈ C(X,E), then X is homeomorphic to Y , and φ is a weighted composition operator. The above conclusio...

Vector-valued elliptic and parabolic boundary value problems subject to general boundary conditions have been investigated recently in [DHP01] in the Lp-context for 1 < p < 1. One of the main goals of this paper was to deduce a maximal Lp-regularity result for the solution of the parabolic initial boundary value problem. A classical reference in the elliptic context are the celebrated papers of...