Motivated by the work of George A. Anastassiou in [George A. Anastassiou, Ostrowski and Landau inequalities for Banach space valued functions, Mathematical and Computer Modelling, 55 (2012), 312–329], we derive some Landau type inequalities for Banach space valued functions without assuming the boundary conditions.

We prove new upper and lower bounds for Banach space-valued stochastic integrals with respect to a compensated Poisson random measure. Our estimates apply to Banach spaces with non-trivial martingale (co)type and extend various results in the literature. We also develop a Malliavin framework to interpret Poisson stochastic integrals as vector-valued Skorohod integrals, and prove a Clark-Ocone r...

Using functional equations, we derive noncommutative extensions of Ramanujan's 1 ψ 1 summation. 1. Introduction. Hypergeometric series with noncommutative parameters and argument, in the special case involving square matrices, have been the subject of recent study, see e.g. the papers by Duval and Ovsienko [DO], Grünbaum [G], Tirao [T], and some of the references mentioned therein. Of course, t...

For finding zeros or fixed points of set-valued maps, the fact that the space of convex, compact, nonempty sets of R is not a vector space presents a major disadvantage. Therefore, fixed point iterations or variants of Newton’s method, in which the derivative is applied only to a smooth single-valued part of the set-valued map, are often applied for calculations. We will embed the set-valued ma...

We determine the computational complexity of the Hahn-Banach Extension Theorem. To do so, we investigate some basic connections between reverse mathematics and computable analysis. In particular, we use Weak König’s Lemma within the framework of computable analysis to classify incomputable functions of low complexity. By defining the multi-valued function Sep and a natural notion of reducibilit...

By using the notion of Jη-proximal mapping for a nonconvex, lower semicontinuous, ηsubdifferentiable proper functional in reflexive Banach spaces, we introduce and study a class of generalized set-valued variational-like inclusions in Banach spaces and show their equivalences with a class of Wiener-Hopf equations. We propose two new iterative algorithms for the class of generalized set-valued v...

We determine the computational complexity of the Hahn-Banach Extension Theorem. To do so, we investigate some basic connections between reverse mathematics and computable analysis. In particular, we use Weak König’s Lemma within the framework of computable analysis to classify incomputable functions of low complexity. By defining the multi-valued function Sep and a natural notion of reducibilit...