An application of fixed point theorem to best approximation in locally convex space

AbstractA common fixed point theorem of Jungck [G. Jungck, On a fixed point theorem of fisher and sessa, Internat. J. Math. Math. Sci., 13 (3) (1990) 497–500] is generalized to locally convex spaces and the new result is applied to extend a result on best approximation

Some Properties of Distances and Best Proximity Points of Cyclic Proximal Contractions in Metric Spaces

This paper presents some results concerning the properties of distances and existence and uniqueness of best proximity points of p-cyclic proximal, weak proximal contractions, and some of their generalizations for the non-self-mapping T:⋃i∈p-Ai→⋃i∈p-Bi  (p≥2), where Ai and Bi, ∀i∈p-={1,2,…,p}, are nonempty subsets of X which satisfy TAi⊆Bi,∀i∈p-, such that (X,d) is a metric space. The boundedness and the convergence of the sequences of distances in the domains and in their respective image sets of the cyclic proximal and weak cyclic proximal non-self-mapping, and of some of their generalizations are investigated. The existence and uniqueness of the best proximity points and the properties of convergence of the iterates to such points are also addressed

On Bounded Strictly Positive Operators of Closed Range and Some Applications to Asymptotic Hyperstability of Dynamic Systems

The problem discussed is the stability of two input-output feedforward and feedback relations, under an integral-type constraint defining an admissible class of feedback controllers. Sufficiency-type conditions are given for the positive, bounded and of closed range feed-forward operator to be strictly positive and then boundedly invertible, with its existing inverse being also a strictly positive operator. The general formalism is first established and the linked to properties of some typical contractive and pseudocontractive mappings while some real-world applications and links of the above formalism to asymptotic hyperstability of dynamic systems are discussed later on

Convergence properties and fixed points of two general iterative schemes with composed maps in banach spaces with applications to guaranteed global stability

This paper investigates the boundedness and convergence properties of two general iterative processes which involve sequences of self-mappings on either complete metric or Banach spaces. The sequences of self-mappings considered in the first iterative scheme are constructed by linear combinations of a set of self-mappings, each of them being a weighted version of a certain primary self-mapping on the same space. The sequences of self-mappings of the second iterative scheme are powers of an iteration-dependent scaled version of the primary self-mapping. Some applications are also given to the important problem of global stability of a class of extended nonlinear polytopic-type parameterizations of certain dynamic systems