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Fixed points of F-weak contractions on complete metric spaces

Wardowski D., Dung N.V.

Demonstratio Mathematica

2014

Vol. 47, nr 1

147--155

In this paper, we introduce the notion of an F-weak contraction and prove a fixed point theorem for F-weak contractions. Examples are given to show that our result is a proper extension of some results known in the literature.

Fixed points for k mappings on a complete metric spaces

Kikina L., Kikina K.

Demonstratio Mathematica

2011

Vol. 44, nr 2

349--357

A fixed point theorem for three mappings on a metric space into itself is proved. This result extends the results obtained in [1] from two mappings to three map pings, and after that, a generalization for an arbitrary number of mappings is obtained. As corollaries of these results we obtain the extending of Theorems of Nesic, Rhoades, Chatterjea, Rus and Kannan for an arbitrary number of mappings.

Stability of solutions for a class of convex minimization problems on reflective Banach spaces

Zaslavski A. J.

Journal of Mathematics and Applications

2008

Vol. 30

151-160

In this paper we study stability of solutions of minimization problems �(x) → min, x ∈ C, where � is a convex lower semicontinuous function and a set C is the countable intersection of a decreasing sequence of closed sets Ci in a reflexive Banach space X.

Asymptotic behavior of inexact orbits for a class of operators in complete metric spaces

Butnariu D., Reich S., Zaslavski A. J.

Journal of Applied Analysis

2007

Vol. 13, nr 1

1-11

We exhibit a class of nonlinear operators with the property that their iterates converge to their unique fixed points even when com- putational errors are present. We also showthat most (in the sense of the Baire category) elements in an appropriate complete metric space of operators do, in fact, possess this property.

Spaces of upper semi-continuous multi-valued functions which are absolute retracts

Uehara S.

Bulletin of the Polish Academy of Sciences. Mathematics

2003

Vol. 51, no 3

319-328

Let X = (X, d] be a metric space. We endow the hyperspace S^X x R consisting of non-empty closed subsets of X x R with the topology induced by d_H defined by d_H(E,F) = inf{epsilon is an element of (0,infinity] | N(E,epsilon) is a subset of F and N(F,epsilon) is a subset E}. Let USCC(X) be a space of upper semi-continuous multi-valued functions phi : X --> R such that phi (x) is a closed interval for every x is an element of X. Identifying those functions with their graphs, we consider USCC(X) as a subspace of 2^X x R. We give a necessary and sufficient condition on X is order that USCC(X) is closed in 2^X x R. In case X is complete, we also give a necessary and sufficient condition on USCC_B(X) to be an AR, where USCC_B(X) is a subspace of USCC(X) consisting of all bounded functions. As a corollary, we find that USCC(X) is an AR if X is compact.