Fixed point theorems in ordered L-spaces

By Adrian Petrusel, Ioan A. Rus. 2005

225 citations recorded by the source corpus.

The purpose of this paper is to present some fixed point results in ordered L-spaces. Our results generalize and extend a recent result of Ran and Reurings (2004). Some applications to matrix equations are also considered.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/10179b7ef91820c47d622e68bc2aea3af1a01641

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In Geometry and Topology

Citations in the corpus

Fixed point theorems for Reich type contractions on metric spaces with a graph (2012, methodology): “The first result in this direction was given by Jachymski [3] who also presented its applications to the Kelisky–Rivlin theorem on iterates of the Bernstein operators on the space C [0, 1].”
Nonlinear contractions involving simulation functions in a metric space with a partial order (2015, result): “Further, several results appeared in this direction, we mention [1, 2, 3, 4, 5, 7, 8, 9, 10, 13] and the references therein.”
Fixed points of Kannan mappings in metric spaces endowed with a graph (2012, background): “Following Petruşel and Rus [10], we say that T is a Picard operator (abbr., PO) if T has a unique fixed point x∗ and lim n→∞ Tnx = x∗ for all x ∈ X and is a weakly Picard operator (abbr.”
Common fixed-point results for nonlinear contractions in ordered partial metric spaces (2011, background): “There exist a vast literature concerning its various generalizations and extensions (see [1-45]).”
Fixed point of φ-contraction in metric spaces endowed with a graph (2010, background): “We refer to Rus [7] and Berinde [2] for a detailed study of ϕ-contractions.”
Fixed point theorems in ordered abstract spaces (2007, methodology): “3 in [4], since orbital continuity can be eliminated if m = 1, obtaining the following result.”
A generalization of Geraghty's theorem in partially ordered metric spaces and applications to ordinary differential equations (2012, background): “The existence of a fixed point, a common fixed point and a couple fixed point for some kinds of contraction type mappings in cone metric spaces, partially ordered metric spaces and fuzzy metric spaces has been considered recently by some authors [1-28] and, by using fixed point theorems, some of the”
Fixed point for set-valued mappings satisfying an implicit relation in partially ordered metric spaces (2009, background): “Recently there have been so many exciting developments in the field of existence of fixed point in partially ordered sets (see [6–16] and the references cited therein).”
Generalized contractions in metric spaces endowed with a graph (2012, background): “Rus [22] by working in the setting of abstract L-spaces in the sense of Fréchet, see for example Theorem 3.”