Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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Now showing 1 - 4 of 4
  • Article
    Citation - WoS: 13
    Citation - Scopus: 20
    Coupled Fixed Point Theorems for Partially Contractive Mappings
    (Springer international Publishing Ag, 2012) Abdeljawad, Thabet
    Recently, some authors have started to generalize fixed point theorems for contractive mappings in a class of generalized metric spaces in which the self-distance need not be zero. These spaces, partial metric spaces, were first introduced by Matthews in 1994. The proved fixed point theorems have been obtained for mappings satisfying contraction type conditions empty of the self-distance. In this article, we prove some coupled fixed point theorems for mappings satisfying contractive conditions allowing the appearance of self-distance terms. These partially contractive mappings do reflect the structure of the partial metric space, and hence their coupled fixed theorems generalize the previously obtained by (Aydi in Int. J. Math. Sci. 2011:Article ID 647091, 2011). Some examples are given to support our claims. MSC: 47H10, 54H25.
  • Article
    Citation - WoS: 80
    Citation - Scopus: 94
    Fixed Points for Generalized Weakly Contractive Mappings in Partial Metric Spaces
    (Pergamon-elsevier Science Ltd, 2011) Abdeljawad, Thabet
    Partial metric spaces were introduced by S. G. Matthews in 1994 as a part of the study of denotational semantics of dataflow networks. In this article, we prove fixed point theorems for generalized weakly contractive mappings on partial metric spaces. These theorems generalize many previously obtained results. An example is given to show that our generalization from metric spaces to partial metric spaces is real. (C) 2011 Elsevier Ltd. All rights reserved.
  • Article
    Citation - WoS: 595
    Citation - Scopus: 680
    On Riemann and Caputo Fractional Differences
    (Pergamon-elsevier Science Ltd, 2011) Abdeljawad, Thabet
    In this paper, we define left and right Caputo fractional sums and differences, study some of their properties and then relate them to Riemann-Liouville ones studied before by Miller K. S. and Ross B., Atici F.M. and Eloe P. W., Abdeljawad T. and Baleanu D., and a few others. Also, the discrete version of the Q-operator is used to relate the left and right Caputo fractional differences. A Caputo fractional difference equation is solved. The solution proposes discrete versions of Mittag-Leffler functions. (C) 2011 Elsevier Ltd. All rights reserved.
  • Article
    Citation - WoS: 6
    Citation - Scopus: 6
    Order Norm Completions of Cone Metric Spaces
    (Taylor & Francis inc, 2011) Abdeljawad, Thabet
    In this article, a completion theorem for cone metric spaces and a completion theorem for cone normed spaces are proved. The completion spaces are constructed by means of an equivalence relation defined via an ordered cone norm on the Banach space E whose cone is strongly minihedral and ordered closed. This order norm has to satisfy the generalized absolute value property. In particular, if E is a Dedekind complete Banach lattice, then, together with its absolute value norm, satisfy the desired properties.