We prove strong convergence of the viscosity approximation process for nonexpansive nonself multimaps. Furthermore, an explicit iteration process which converges strongly to a fixed point of multimap T is constructed. It is worth... more
It is commonly accepted that optimal control theory was born with the publication of a seminal paper by Pontryagin and collaborates last century, at the end of 50's. Since then optimal control theory has played a relevant role not only in... more
In this paper, we construct a new iterative scheme by hybrid method for approximation of common element of set of common fixed points of countably infinite family of relatively quasi-nonexpansive mappings and set of common solutions to a... more
Let T : D ⊂ X → X be an iteration function in a complete metric space X . In this paper we present some new general complete convergence theorems for the Picard iteration x n+1 = Tx n with order of convergence at least r ≥ 1. Each of... more
We consider the prediction problem of a continuous-time stochastic process on an entire time-interval in terms of its recent past. The approach we adopt is based on the notion of autoregressive Hilbert processes that represent a... more
General local convergence theorems with order of convergence r ≥ 1 are provided for iterative processes of the type x n+1 = Tx n , where T : D ⊂ X → X is an iteration function in a metric space X . The new local convergence theory is... more
We discuss some open problems in the Geometry of Banach spaces having Ramsey-theoretic flavor. The problems are exposed together with well known results related to them.
We study a class of third-order iterative methods for nonlinear equations on Banach spaces. A characterization of the convergence under Kantorovich type conditions and optimal estimates of the error are found. Though, in general, these... more
We introduce a new method to derive lower bounds on randomized and quantum communication complexity. Our method is based on factorization norms, a notion from Banach Space theory. This approach gives us access to several powerful tools... more
In many physical phenomena, especially in temperature over-specification partial differential equation with an unknown source function appears. The present paper is devoted to the study of the well-posedness of the approximate solution of... more
We obtain general lower and upper estimates for the first and the second Bohr radii of bounded complete Reinhardt domains in C n : r 2004 Elsevier Inc. All rights reserved.
We characterize the existence and uniqueness of solutions of an abstract fractional differential equation with infinite delay in Hölder spaces.
Let A and M be closed linear operators defined on a complex Banach space X. Using operator-valued Fourier multipliers theorems, we obtain necessary and sufficient conditions to guarantee existence and uniqueness of periodic solutions to... more
We consider variable stepsize time approximations of holomorphic semigroups on general Banach spaces. For strongly A(0)-acceptable rational functions a general stability theorem is proved, which does not impose any constraint on the... more
Fixed point problems Generalized mixed equilibrium problem Hammerstein equations Monotone operators Uniformly convex and uniformly smooth Banach spaces Weak relatively nonexpansive mappings a b s t r a c t
In this paper we prove the stability of semidiscretizations in time of holomorphic semigroups in Banach spaces by means of A(a)-stable rational multistep methods. No assumptions on the method other than A(a)-stability are required. Our... more
In this paper, we study the functional equation, f ( x + y ) - f ( x ) f ( y ) = d sin x sin y . Some generalizations of the above functional equation are also considered.
This paper deals with the conditions for a vector norm to be a Lyapunov function for a linear time-invariant system. An error in the proof of the related theorem given in [5] is pointed out, and a counterexample proving that this theorem... more
This paper is devoted to the study of relationships between solutions of Stampacchia and Minty vector variational-like inequalities, weak and strong Pareto solutions of vector optimization problems and vector critical points in Banach... more
Regularization methods for inverse problems formulated in Hilbert spaces usually give rise to over-smoothness, which does not allow to obtain a good contrast and localization of the edges in the context of image restoration. On the other... more
Extending a classical linear result due to Hutton to a nonlinear setting, we prove that a continuous homogeneous polynomial between Banach spaces can be approximated by finite rank polynomials if and only if its adjoint can be... more
This article investigates some modiÿcation of the Navier-Stokes equations of type as the modiÿcation that was suggested by Lions (Quelques Methodes de Resolution des Problemes aux Limites Non Lineares, DUNOD, Gauthier-Villaris, Paris, 1969)
a b s t r a c t In this paper, we extend the auxiliary variational inequality technique due to Ding and Yao [X.P. Ding, J.C. Yao, Existence and algorithm of solutions for mixed quasi-variationallike inclusions in Banach spaces, Comput.... more
Let U and V be convex and balanced open subsets of the Banach spaces X and Y respectively. In this paper we study the following question: Given two Fréchet algebras of holomorphic functions of bounded type on U and V respectively that are... more
Using Smolyak's construction , we derive a new algorithm for approximating multivariate functions over bounded or unbounded regions in R s with the error measured in a weighted L 1 -norm. We provide upper bounds for the algorithm's cost... more
Initial boundary value problems (IBVPs) u (t) = Au(t) + f (t), ∂u(t) = g(t), 0 t T , u(0) = u 0 , where A : D(A) ⊂ X → X and ∂ : D(A) ⊂ X → Y are linear, densely defined operators and X and Y are Banach spaces, are considered. These IBVPs... more
Random networks of nonlinear functions have a long history of empirical success in function fitting but few theoretical guarantees. In this paper, using techniques from probability on Banach Spaces, we analyze a specific architecture of... more
We study sparse approximation by greedy algorithms. Our contribution is twofold. First, we prove exact recovery with high probability of random K-sparse signals within ⌈K(1 + ǫ)⌉ iterations of the Orthogonal Matching Pursuit (OMP). This... more
We analyze Tikhonov regularization where the forward operator is defined on a direct sum U of several Banach spaces U i ; i ¼ 1; . . . ; m. The regularization term on U is a sum of different regularizations on each U i . The theoretical... more
Motivated by an old paper of Wells [J. London Math. Soc. 2 (1970), 549-556] we define the space X ⊗Y , where X and Y are "homogeneous" Banach spaces of analytic functions on the unit disk D, by the requirement that f can be represented as... more
This paper deals with approximate value iteration (AVI) algorithms applied to discounted dynamic (DP) programming problems. The so-called Bellman residual is shown to be convex in the Banach space of candidate solutions to the DP problem.... more
We characterize generalized bi-circular projections on I(H), a minimal norm ideal of operators in B(H), where H is a separable infinite dimensional Hilbert space.
In previous works valuable tools in testing statistical hypotheses about the mean of the fuzzy random variable have been developed. In this paper we present a study about the power function of an asymptotic procedure for the one-sample... more
In this note, we characterize nice operators in a class of Banach spaces, which includes spaces C(K) and L 1 (µ), as those operators that preserve extreme points.
We examine the Poisson equation with boundary conditions on a cylinder in a weighted space of L p , p ≥ 3, type. The weight is a positive power of the distance from a distinguished plane. To prove the existence of solutions we use our... more
The second order of accuracy difference scheme for the approximate solutions of the nonlocal boundary-value problem −v (t) + Av(t) = f (t) (0 ≤ t ≤ 1), v(0) = v(1), v (0) = v (1) for differential equations in an arbitrary Banach space E... more
Let A be the generator of an immediately norm continuous C0-semigroup defined on a Banach space X. We study the existence and uniqueness of bounded solutions for the semilinear integro-differential equation with infinite delay
The behavior of bilinear operators acting on interpolation of Banach spaces for the ρρ method in relation to the compactness is analyzed. Similar results of Lions-Peetre, Hayakawa and Persson’s compactness theorems are obtained for the... more
An extension to an L p -spaces, p > 1, of Pearson-Kolmogorov-Renyi correlation ratio is constructed. It is proved that correlation does not exceed 2 2 p −1 , and can be used as a measure of dependence of the random variable from a... more
In this paper we show that the well-known Mönch fixed point theorem for non-self mappings remains valid if we replace the Leray-Schauder boundary condition by the interior condition. As a consequence, we obtain a partial generalization of... more
We show a fixed point theorem for condensing mappings under a new condition of the Leray-Schauder type. We call it the Interior Condition. We also discuss examples that demonstrate the independence of these two conditions.
In this paper we consider continuity properties of a stochastic heat equation of the form &(f,x)/lZt = a2u(t,x),/3x2 +f(u(t..x))W,,,. We prove that the solutions of this equation depend continuously on the functionf'and give some new... more
The paper argues strongly in favour of the opinion that Kantian pure reason could be implemented via pure mathematics to reveal a true deep aspect of the fundamental monads of the real physics of the cosmos. Thus using a remarkable pure... more
Let F be a mapping from a complex Banach space into another complex Banach space with a Schauder basis, such that each coordinate composition mapping is holomorphic. Necessary and sufficient conditions are given that F be holomorphic.
A new algorithm for the reconstruction of sparse signals from noise corrupted compressed measurements is presented. The algorithm is based on minimizing an ℓp,ϵ-norm regularized ℓ2 error. The minimization is carried out by iteratively... more
This paper considers techniques for creating enhanced resolution images from irregular samples, with specific application to imaging from scatterometers. Using previously established irregular sampling theory, and developing the idea of... more
By using a norm generated by the error series of a sequence of interpolation polynomials, we obtain in this paper ~ertain Banach spaces. A relation between these spaces and the space (Co, S) with norm generated by the error series of the... more
We investigate pointwise nonnegativity as an obstruction to various types of structured completeness in $L^p(\R)$. For example, we prove that if each element of the system $\{f_n\}_{n=1}^\infty \subset L^p(\R)$ is pointwise nonnegative,... more