On the convergence theorems for a countable family of Lipschitzian pseudocontraction mappings in Banach spaces.
On the Converse of Caristi's Fixed Point Theorem
Let X be a nonempty set of cardinality at most and T be a selfmap of X. Our main theorem says that if each periodic point of T is a fixed point under T, and T has a fixed point, then there exist a metric d on X and a lower semicontinuous map ϕ :X→ ℝ ₊ such that d(x,Tx) ≤ ϕ(x) - ϕ(Tx) for all x∈ X, and (X,d) is separable. Assuming CH (the Continuum Hypothesis), we deduce that (X,d) is compact.
On the correct formulation of a nonlinear differential equation in Banach spaces.
On the Cosine-Sine Operator Functional Equations
On the Cosine-Sine Operator Functional Equations (Short Communication)
On the covering dimension of the fixed point set of certain multifunctions
We study the covering dimension of the fixed point set of lower semicontinuous multifunctions of which many values can be non-closed or non-convex. An application to variational inequalities is presented.
On the cyclic elements of the shift operator in a weighted anisotropic space of holomorphic function in the polydisc.
On the (C,α) Cesàro bounded operators
For a given linear operator T in a complex Banach space X and α ∈ ℂ with ℜ (α) > 0, we define the nth Cesàro mean of order α of the powers of T by . For α = 1, we find , the usual Cesàro mean. We give necessary and sufficient conditions for a (C,α) bounded operator to be (C,α) strongly (weakly) ergodic.
On the (C,α) uniform ergodic theorem
We improve a recent result of T. Yoshimoto about the uniform ergodic theorem with Cesàro means of order α. We give a necessary and sufficient condition for the (C,α) uniform ergodicity with α > 0.
On the Davis-Kahan-Weinberger Solution of the Norm-Preserving Dilation Problem.
On the defect spectrum of an extension of a Banach space operator
Let be an operator acting on a Banach space . We show that between extensions of to some Banach space which do not increase the defect spectrum (or the spectrum) it is possible to find an extension with the minimal possible defect spectrum.
On the definition of fuzzy Hilbert spaces and its application.
On the degree theory for densely defined mappings of class .
On the density of extremal solutions of differential inclusions
An existence theorem for the cauchy problem (*) ẋ ∈ ext F(t,x), x(t₀) = x₀, in banach spaces is proved, under assumptions which exclude compactness. Moreover, a type of density of the solution set of (*) in the solution set of ẋ ∈ f(t,x), x(t₀) = x₀, is established. The results are obtained by using an improved version of the baire category method developed in [8]-[10].
On the dependence of the orthogonal projector on deformations of the scalar product
We consider scalar products on a given Hilbert space parametrized by bounded positive and invertible operators defined on this space, and orthogonal projectors onto a fixed closed subspace of the initial Hilbert space corresponding to these scalar products. We show that the projector is an analytic function of the scalar product, we give the explicit formula for its Taylor expansion, and we prove some algebraic formulas for projectors.
On the diagonal of matrix transformations
On the differences of the consecutive powers of Banach algebra elements
Let A denote a complex unital Banach algebra. We characterize properties such as boundedness, relative compactness, and convergence of the sequence for an arbitrary x ∈ A, using σ(x) and resolvent conditions. Under these circumstances, we investigate elements in the peripheral spectrum, and give further conclusions, also involving the behaviour of and .
On the differentiability of functions of an operator
On the differentiability of mappings and convex functionals
On the differentiability of mappings and convex functionals: A correction