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

  1. Research Article

    Moduli and Characteristics of Monotonicity in Some Banach Lattices

    First the characteristic of monotonicity of any Banach lattice http://static-content.springer.com/image/art%3A10.1155%2F2010%2F852346/MediaObjects/13663_2009_Article_1355_IEq1_HTML.gif is expressed in terms of the left limit of the modulus of monotonicity o...

    Paweł Foralewski, Henryk Hudzik, Radosław Kaczmarek and Miroslav Krbec

    Fixed Point Theory and Applications 2010 2010:852346

    Published on: 31 May 2010

  2. Research Article

    On Some Properties of Hyperconvex Spaces

    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...

    Marcin Borkowski, Dariusz Bugajewski and Dev Phulara

    Fixed Point Theory and Applications 2010 2010:213812

    Published on: 24 February 2010

  3. Research Article

    Fixed Point Theorems for Set-Valued Contraction Type Maps in Metric Spaces

    We first give some fixed point results for set-valued self-map contractions in complete metric spaces. Then we derive a fixed point theorem for nonself set-valued contractions which are metrically inward. Our ...

    A Amini-Harandi and D O'Regan

    Fixed Point Theory and Applications 2010 2010:390183

    Published on: 14 February 2010

  4. Research Article

    Approximating Fixed Points of Some Maps in Uniformly Convex Metric Spaces

    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...

    AbdulRahim Khan, Hafiz Fukhar-ud-din and AbdulAziz Domlo

    Fixed Point Theory and Applications 2010 2010:385986

    Published on: 26 January 2010

  5. Research Article

    A Continuation Method for Weakly Kannan Maps

    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 ...

    David Ariza-Ruiz and Antonio Jiménez-Melado

    Fixed Point Theory and Applications 2010 2010:321594

    Published on: 26 January 2010

  6. Research Article

    Generalized IFSs on Noncompact Spaces

    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...

    Alexandru Mihail and Radu Miculescu

    Fixed Point Theory and Applications 2010 2010:584215

    Published on: 21 January 2010

  7. Research Article

    Fixed Point Theorems on Spaces Endowed with Vector-Valued Metrics

    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...

    Alexandru-Darius Filip and Adrian Petruşel

    Fixed Point Theory and Applications 2010 2010:281381

    Published on: 17 January 2010

  8. Research Article

    Does Kirk's Theorem Hold for Multivalued Nonexpansive Mappings?

    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...

    T Domínguez Benavides and B Gavira

    Fixed Point Theory and Applications 2010 2010:546761

    Published on: 17 January 2010

  9. Research Article

    Fixed Points for Discontinuous Monotone Operators

    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...

    Yujun Cui and Xingqiu Zhang

    Fixed Point Theory and Applications 2009 2010:926209

    Published on: 24 December 2009

  10. Research Article

    Halpern's Iteration in CAT(0) Spaces

    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...

    Satit Saejung

    Fixed Point Theory and Applications 2009 2010:471781

    Published on: 7 December 2009

  11. Research Article

    Periodic Point, Endpoint, and Convergence Theorems for Dissipative Set-Valued Dynamic Systems with Generalized Pseudodistances in Cone Uniform and Uniform Spaces

    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...

    Kazimierz Włodarczyk and Robert Plebaniak

    Fixed Point Theory and Applications 2009 2010:864536

    Published on: 19 November 2009

  12. Research Article

    Fixed Points for Pseudocontractive Mappings on Unbounded Domains

    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...

    Jesús García-Falset and E Llorens-Fuster

    Fixed Point Theory and Applications 2009 2010:769858

    Published on: 18 October 2009

  13. Research Article

    Coincidence Theorems for Certain Classes of Hybrid Contractions

    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 ...

    SL Singh and SN Mishra

    Fixed Point Theory and Applications 2009 2010:898109

    Published on: 13 October 2009

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