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Erdal Karapınar - One of the best experts on this subject based on the ideXlab platform.

  • Quadruple fixed point theorems for nonlinear contractions on partial metric spaces
    Applied General Topology, 2014
    Co-Authors: Erdal Karapınar, Kenan Taş
    Abstract:

    The notion of coupled fixed point was introduced by Guo and Laksmikantham [12]. Later Gnana Bhaskar and Lakshmikantham in [11] investigated the coupled fixed points in the setting of partially ordered set by defining the notion of mixed monotone property. Very recently, the concept of tripled fixed point was introduced by Berinde and Borcut [7]. Following this trend, Karapinar[19] defined the quadruple fixed point. In this manuscript, quadruple fixed point is discussed and some new fixed point theorems are obtained on partial metric spaces.

  • Multidimensional Fixed-Point Theorems in Partially Ordered Complete Partial Metric Spaces under ()-Contractivity Conditions
    Abstract and Applied Analysis, 2013
    Co-Authors: A. Roldán, Juan Martínez-moreno, C. Roldán, Erdal Karapınar
    Abstract:

    We study the existence and uniqueness of coincidence point for nonlinear mappings of any number of arguments under a weak ( )-contractivity condition in partial metric spaces. The results we obtain generalize, extend, and unify several classical and very recent related results in the literature in metric spaces (see Aydi et al. (2011), Berinde and Borcut (2011), Gnana Bhaskar and Lakshmikantham (2006), Berzig and Samet (2012), Borcut and Berinde (2012), Choudhury et al. (2011), Karapinar and Luong (2012), Lakshmikantham and Ciric (2009), Luong and Thuan (2011), and Roldan et al. (2012)) and in partial metric spaces (see Shatanawi et al. (2012)).

  • Quadruple fixed point theorems for nonlinear contractions
    Computers & Mathematics with Applications, 2012
    Co-Authors: Erdal Karapınar, Nguyen Van Luong
    Abstract:

    The notion of coupled fixed point is introduced by Gnana-Bhaskar and Lakshmikantham. Very recently, the concept of tripled fixed point was introduced by Berinde and Borcut. In this manuscript, a quadruple fixed point is considered and some new related fixed point theorems are obtained. We also give some examples to illustrate our results.

  • Quadruple Fixed Point Theorems for Weak ϕ-Contractions
    ISRN Mathematical Analysis, 2011
    Co-Authors: Erdal Karapınar
    Abstract:

    The notion of coupled fixed point is introduced in by Gnana Bhaskar and Lakshmikantham (2006). Very recently, the concept of tripled fixed point is introduced by Berinde and Borcut (2011). In this paper, quadruple fixed point is introduced, and some new fixed point theorems are obtained.

  • Quartet fixed point for nonlinear contraction
    arXiv: General Topology, 2011
    Co-Authors: Erdal Karapınar
    Abstract:

    The notion of coupled fixed point is introduced in by Bhaskar and Lakshmikantham in [2]. Very recently, the concept of tripled fixed point is introduced by Berinde and Borcut [1]. In this manuscript, by using the mixed g monotone mapping, some new quartet fixed point theorems are obtained. We also give some examples to support our results.

Stojan Radenović - One of the best experts on this subject based on the ideXlab platform.

Isabel Marrero - One of the best experts on this subject based on the ideXlab platform.

  • Weak compactness and the Eisenfeld-Lakshmikantham measure of nonconvexity
    Fixed Point Theory and Applications, 2012
    Co-Authors: Isabel Marrero
    Abstract:

    In this article, weakly compact subsets of real Banach spaces are characterized in terms of the Cantor property for the Eisenfeld-Lakshmikantham measure of nonconvexity. This characterization is applied to prove the existence of fixed points for condensing maps, nonexpansive maps, and isometries without convexity requirements on their domain. Mathematics Subject Classification 2010: Primary 47H10; Secondary 46B20, 47H08, 47H09.

  • A note on reflexivity and nonconvexity
    Nonlinear Analysis: Theory Methods & Applications, 2011
    Co-Authors: Isabel Marrero
    Abstract:

    Abstract In this short note we prove that a Banach space X is reflexive if, and only if, the Eisenfeld–Lakshmikantham measure of nonconvexity in X satisfies the Cantor property. Using this characterization, some results in best approximation and fixed point theory for reflexive Banach spaces are generalized by removing convexity requirements.

  • Measures of Noncircularity and Fixed Points of Contractive Multifunctions
    Fixed Point Theory and Applications, 2010
    Co-Authors: Isabel Marrero
    Abstract:

    In analogy to the Eisenfeld-Lakshmikantham measure of nonconvexity and the Hausdorff measure of noncompactness, we introduce two mutually equivalent measures of noncircularity for Banach spaces satisfying a Cantor type property, and apply them to establish a fixed point theorem of Darbo type for multifunctions. Namely, we prove that every multifunction with closed values, defined on a closed set and contractive with respect to any one of these measures, has the origin as a fixed point.

Madjid Eshaghi Gordji - One of the best experts on this subject based on the ideXlab platform.

D. D. Bainov - One of the best experts on this subject based on the ideXlab platform.

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