Search results for "MultiValue"
showing 10 items of 25 documents
Fixed Points for Multivalued Convex Contractions on Nadler Sense Types in a Geodesic Metric Space
2019
In 1969, based on the concept of the Hausdorff metric, Nadler Jr. introduced the notion of multivalued contractions. He demonstrated that, in a complete metric space, a multivalued contraction possesses a fixed point. Later on, Nadler&rsquo
On the stability of spline-collocation methods of multivalue type
1987
In this paper the general classV of spline-collocation methods for first order systems of ordinary differential equations is investigated. The methods can in part be regarded as so-called multivalue methods. This type contains the generalized singly-implicit methods treated by Butcher.
A-stable spline-collocation methods of multivalue type
1989
In this paper the general classV of spline-collocation methods presented by Multhei is investigated. The methods ofV approximate solutions of first order initial value problems. ClassV contains as subclass the methods of so-called multivalue type, and in particular contains the generalized singly-implicit methods treated by Butcher.
On dependence of sets of functions on the mean value of their elements
2009
The paper considers, for a given closed bounded set M ⊂ R m and K = (0,1) n ⊂ R n , the set M = {h ϵ L2 (K;R m ) | h(x) ϵ M a.e.x ϵ K} and its subsets It is shown that, if a sequence {hk } ⊂ coM converges to an element hk ϵ M(hk ) there is h‘k ϵ M(ho ) such that h'k - hk → 0 as k → ∞ . If, in addition, the set M is finite or M is the convex hull of a finite set of elements, then the multivalued mapping h → M(h) is lower semicontinuous on coM. First published online: 14 Oct 2010
Multi-integrals of finite variation
2020
The aim of this paper is to investigate different types of multi-integrals of finite variation and to obtain decomposition results.
Fixed points for multivalued mappings in b-metric spaces
2015
In 2012, Samet et al. introduced the notion ofα-ψ-contractive mapping and gave sufficient conditions for the existence of fixed points for this class of mappings. The purpose of our paper is to study the existence of fixed points for multivalued mappings, under anα-ψ-contractive condition of Ćirić type, in the setting of completeb-metric spaces. An application to integral equation is given.
Caristi Type Selections of Multivalued Mappings
2015
Multivalued mappings and related selection theorems are fundamental tools in many branches of mathematics and applied sciences. In this paper we continue this theory and prove the existence of Caristi type selections for generalized multivalued contractions on complete metric spaces, by using some classes of functions. Also we prove fixed point and quasi-fixed point theorems.
A generalization of Nadler fixed point theorem
2015
Jleli and Samet gave a new generalization of the Banach contraction principle in the setting of Branciari metric spaces [Jleli, M. and Samet, B., A new generalization of the Banach contraction principle, J. Inequal. Appl., 2014:38 (2014)]. The purpose of this paper is to study the existence of fixed points for multivalued mappings, under a similar contractive condition, in the setting of complete metric spaces. Some examples are provided to illustrate the new theory.
Proper 1-ball contractive retractions in Banach spaces of measurable functions
2005
In this paper we consider the Wosko problem of evaluating, in an infinite-dimensional Banach space X, the infimum of all k > 1 for which there exists a k-ball contractive retraction of the unit ball onto its boundary. We prove that in some classical Banach spaces the best possible value 1 is attained. Moreover we give estimates of the lower H-measure of noncompactness of the retractions we construct. 1. Introduction Let X be an infinite-dimensional Banach space with unit closed ball B(X) and unit sphere S(X). It is well known that, in this setting, there is a retraction of B(X) onto S(X), that is, a continuous mapping R : B(X) ! S(X) with Rx = x for all x 2 S(X). In (4) Benyamini and Sternf…