Related papers: On summability, integrability and impulsive differ…
In this paper, we introduce new implicit and explicit iterative schemes which converge strongly to a unique solution of variational inequality problems for strongly accretive operators over a common fixed point set of finite family of…
We generalize the notion of summable Szlenk index from a Banach space to an arbitrary weak$^*$-compact set. We prove that a weak$^*$-compact set has summable Szlenk index if and only if its weak$^*$-closed, absolutely convex hull does. As a…
Certain previously known upper bounds on the moments of the norm of martingales in 2-smooth Banach spaces are improved. Some of these improvements hold even for sums of independent real-valued random variables. Applications to concentration…
We suggest an approach for description of integrable cases of the Abel equations. It is based on increasing of the order of equations up to the second one and using equivalence transformations for the corresponding second-order ordinary…
A Banach algebra A is self-induced if the multiplication is an isomorphism from the A-balanced projective tensor-square of A to A. The class of self-induced Banach algebras is a natural generalization of unital Banach algebras, providing a…
We study a local version of the ball-covering problem in Banach spaces, and obtain a complete solution to it in terms of the norm derivatives. We illustrate the advantage of the local approach by obtaining substantial refinements of several…
In this note we define summable families in tempered distribution spaces and we state some their properties and characterizations. Summable families are the analogous of summable sequences in separable Hilbert spaces, but in tempered…
In this paper, using the monotone iterative technique and the Banach contraction mapping principle, we study a class of fractional differential system with integral boundary on an infinite interval. Some explicit monotone iterative schemes…
M. Daher gave conditions so that the spheres of the spaces in the interior of a complex interpolation scale are uniformly homeomorphic. We look for sufficient conditions for the validity of this result and related ones on the extremes of…
In this article, we first try to make the known analogy between convexity and plurisubharmonicity more precise. Then we introduce a notion of strict plurisubharmonicity analogous to strict convexity, and we show how this notion can be used…
In this paper, using generalized metric projection, we propose a new extragradient method for finding a common element of the solutions set of a generalized equilibrium problem and a variational inequality for an $\alpha$-inverse-strongly…
In this paper, we deal with a notion of Banach space-valued mappings defined on a set consisting of finite graphs with uniformly bounded vertex degree. These functions will be endowed with certain boundedness and additivity criteria. We…
In this paper, the local convergence of Iteratively regularized Landweber iteration method is investigated for solving non-linear inverse problems in Banach spaces. Our analysis mainly relies on the assumption that the inverse mapping…
Consider a smooth vector field $f\colon \mathbb{R}^n\to\mathbb{R}^n$ and a maximal solution $\gamma\colon \,]a,b[\,\to \mathbb{R}^n$ to the ordinary differential equation $x'=f(x)$. It is a well-known fact that, if $\gamma$ is bounded, then…
Unique continuation properties for a class of evolution equations defined on Banach spaces are considered from two different point of views: the first one is based on the existence of conserved quantities, which very often translates into…
These notes concern the nonlinear geometry of Banach spaces, asymptotic uniform smoothness and several Banach-Saks-like properties. We study the existence of certain concentration inequalities in asymptotically uniformly smooth Banach…
This article investigates the approximate controllability of second order non-autonomous functional evolution equations involving non-instantaneous impulses and nonlocal conditions. First, we discuss the approximate controllability of…
The concept of moment differentiation is extended to the class of moment summable functions, giving rise to moment differential properties. The main result leans on accurate upper estimates for the integral representation of the moment…
We give a rate of metastability for Halpern's iteration relative to a rate of metastability for the resolvent for nonexpansive mappings in uniformly smooth Banach spaces, extracted from a proof due to Xu. In Hilbert space, the latter is…
We consider ill-posed linear operator equations with operators acting between Banach spaces. For solution approximation, the methods of choice here are projection methods onto finite dimensional subspaces, thus extending existing results…