Finite-dimensional subspaces of uniformly convex and uniformly smooth Banach lattices and trace classes
Finite-rank intermediate Hankel operators on the Bergman space.
Finite-rank perturbations of positive operators and isometries
We completely characterize the ranks of A - B and for operators A and B on a Hilbert space satisfying A ≥ B ≥ 0. Namely, let l and m be nonnegative integers or infinity. Then l = rank(A - B) and for some operators A and B with A ≥ B ≥ 0 on a Hilbert space of dimension n (1 ≤ n ≤ ∞) if and only if l = m = 0 or 0 < l ≤ m ≤ n. In particular, this answers in the negative the question posed by C. Benhida whether for positive operators A and B the finiteness of rank(A - B) implies that of . For...
Finite-step relaxed hybrid steepest-descent methods for variational inequalities.
Firmly pseudo-contractive mappings and fixed points
We give some fixed point theorems for firmly pseudo-contractive mappings defined on nonconvex subsets of a Banach space. We also prove some fixed point results for firmly pseudo-contractive mappings with unbounded nonconvex domain in a reflexive Banach space.
First integrals for problems of calculus of variations on locally convex spaces.
First order impulsive differential inclusions with periodic conditions.
First results on spectrally bounded operators
A linear mapping T from a subspace E of a Banach algebra into another Banach algebra is defined to be spectrally bounded if there is a constant M ≥ 0 such that r(Tx) ≤ Mr(x) for all x ∈ E, where r(·) denotes the spectral radius. We study some basic properties of this class of operators, which are sometimes analogous to, sometimes very different from, those of bounded operators between Banach spaces.
First-order differential equations of the hyperbolic type.
Five equivalent theorems on a convex subset of a topological vector space
Fixed and coincidence points of hybrid mappings
The purpose of this note is to provide a substantial improvement and appreciable generalizations of recent results of Beg and Azam; Pathak, Kang and Cho; Shiau, Tan and Wong; Singh and Mishra.
Fixed edge theorems for complete lattices
Fixed point analysis for non-oscillatory solutions of quasi linear ordinary differential equations
The paper deals with the quasi-linear ordinary differential equation with . We treat the case when is not necessarily monotone in its second argument and assume usual conditions on and . We find necessary and sufficient conditions for the existence of unbounded non-oscillatory solutions. By means of a fixed point technique we investigate their growth, proving the coexistence of solutions with different asymptotic behaviors. The results generalize previous ones due to Elbert–Kusano, [Acta...
Fixed point and coincidence point theorems for a pair of single-valued and multi-valued maps on a metric space.
Fixed point and continuation results for contractions in metric and gauge spaces
We present an overview of generalizations of Banach's fixed point theorem and continuation results for contractions, i.e., results establishing that the existence of a fixed point is preserved by suitable homotopies. We will consider single-valued and multi-valued contractions in metric and in gauge spaces.
Fixed point and homotopy result for mappings satisfying an implicit relation
In this paper, we prove some fixed point theorems for single valued mappings satisfying an implicit relation on space with two metrics. In addition we give a homotopy result using our theorems.
Fixed point and multidimensional fixed point theorems with applications to nonlinear matrix equations in terms of weak altering distance functions
The aim of this work is to introduce the notion of weak altering distance functions and prove new fixed point theorems in metric spaces endowed with a transitive binary relation by using weak altering distance functions. We give some examples which support our main results where previous results in literature are not applicable. Then the main results of the paper are applied to the multidimensional fixed point results. As an application, we apply our main results to study a nonlinear matrix equation....
Fixed point approximation of weakly commuting mappings in Banach space.
Fixed point approximation under Mann iteration beyond Ishikawa
Consider the Mann iteration for a nonexpansive mapping defined on some subset of the normed space . We present an innovative proof of the Ishikawa almost fixed point principle for nonexpansive mapping that reveals deeper aspects of the behavior of the process. This fact allows us, among other results, to derive convergence of the process under the assumption of existence of an accumulation point of .
Fixed point free maps of a closed ball with small measures of noncompactness.
We show that in all infinite-dimensional normed spaces it is possible to construct a fixed point free continuous map of the unit ball whose measure of noncompactness is bounded by 2. Moreover, for a large class of spaces (containing separable spaces, Hilbert spaces and l-infinity (S)) even the best possible bound 1 is attained for certain measures of noncompactness.