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Impact of Kirk's Results on the Development of Fixed Point Theory

  1. Given a tangent vector field on a finite-dimensional real smooth manifold, its degree (also known as characteristic or rotation) is, in some sense, an algebraic count of its zeros and gives useful information for...

    Authors: Massimo Furi, MariaPatrizia Pera and Marco Spadini
    Citation: Fixed Point Theory and Applications 2010 2010:845631
  2. We are going to answer some open questions in the theory of hyperconvex metric spaces. We prove that in complete http://static-content.springer.com/image/art%3A10.1155%2F2010%2F213812/MediaObjects/13663_2009_Article_1227_IEq1_HTML.gif -trees hyperconvex hull...

    Authors: Marcin Borkowski, Dariusz Bugajewski and Dev Phulara
    Citation: Fixed Point Theory and Applications 2010 2010:213812
  3. We study strong convergence of the Ishikawa iterates of qasi-nonexpansive (generalized nonexpansive) maps and some related results in uniformly convex metric spaces. Our work improves and generalizes the corre...

    Authors: AbdulRahim Khan, Hafiz Fukhar-ud-din and AbdulAziz Domlo
    Citation: Fixed Point Theory and Applications 2010 2010:385986
  4. The first continuation method for contractive maps in the setting of a metric space was given by Granas. Later, Frigon extended Granas theorem to the class of weakly contractive maps, and recently Agarwal and ...

    Authors: David Ariza-Ruiz and Antonio Jiménez-Melado
    Citation: Fixed Point Theory and Applications 2010 2010:321594
  5. The aim of this paper is to continue the research work that we have done in a previous paper published in this journal (see Mihail and Miculescu, 2008). We introduce the notion of GIFS, which is a family of fu...

    Authors: Alexandru Mihail and Radu Miculescu
    Citation: Fixed Point Theory and Applications 2010 2010:584215
  6. Fixed Point Theory for multivalued mappings has many useful applications in Applied Sciences, in particular, in Game Theory and Mathematical Economics. Thus, it is natural to try of extending the known fixed p...

    Authors: T Domínguez Benavides and B Gavira
    Citation: Fixed Point Theory and Applications 2010 2010:546761
  7. The purpose of this work is to present some (local and global) fixed point results for singlevalued and multivalued generalized contractions on spaces endowed with vector-valued metrics. The results are extens...

    Authors: Alexandru-Darius Filip and Adrian Petruşel
    Citation: Fixed Point Theory and Applications 2010 2010:281381
  8. We establish two fixed point theorems for nonlinear operators on Banach spaces partially ordered by a cone. The first fixed point theorem is concerned with a class of mixed monotone operators. In the second fi...

    Authors: Hui-Sheng Ding, Jin Liang and Ti-Jun Xiao
    Citation: Fixed Point Theory and Applications 2010 2010:108343
  9. We obtain some new existence theorems of the maximal and minimal fixed points for discontinuous monotone operator on an order interval in an ordered normed space. Moreover, the maximal and minimal fixed points...

    Authors: Yujun Cui and Xingqiu Zhang
    Citation: Fixed Point Theory and Applications 2009 2010:926209
  10. With a recent result of Suzuki (2001) we extend Caristi-Kirk's fixed point theorem, Ekeland's variational principle, and Takahashi's minimization theorem in a complete metric space by replacing the distance wi...

    Authors: Zili Wu
    Citation: Fixed Point Theory and Applications 2009 2010:970579
  11. Motivated by Halpern's result, we prove strong convergence theorem of an iterative sequence in CAT(0) spaces. We apply our result to find a common fixed point of a family of nonexpansive mappings. A convergenc...

    Authors: Satit Saejung
    Citation: Fixed Point Theory and Applications 2009 2010:471781
  12. In cone uniform and uniform spaces, we introduce the three kinds of dissipative set-valued dynamic systems with generalized pseudodistances and not necessarily lower semicontinuous entropies, we study the conv...

    Authors: Kazimierz Włodarczyk and Robert Plebaniak
    Citation: Fixed Point Theory and Applications 2009 2010:864536
  13. We give some fixed point results for pseudocontractive mappings on nonbounded domains which allow us to obtain generalizations of recent fixed point theorems of Penot, Isac, and Németh. An application to integ...

    Authors: Jesús García-Falset and E Llorens-Fuster
    Citation: Fixed Point Theory and Applications 2009 2010:769858
  14. Coincidence and fixed point theorems for a new class of hybrid contractions consisting of a pair of single-valued and multivalued maps on an arbitrary nonempty set with values in a metric space are proved. In ...

    Authors: SL Singh and SN Mishra
    Citation: Fixed Point Theory and Applications 2009 2010:898109
  15. We study the existence of fixed points and convergence of iterates for asymptotic pointwise contractions in uniformly convex metric spaces. We also study the existence of fixed points for set-valued nonexpansi...

    Authors: Rafa Espínola, Aurora Fernández-León and Bożena Piątek
    Citation: Fixed Point Theory and Applications 2009 2010:169837