445 research outputs found
Coupled fixed point theorems for generalized symmetric Meir--Keeler contractions in ordered metric spaces
In this paper we introduce generalized symmetric Meir-Keeler contractions and
prove some coupled fixed point theorems for mixed monotone operators in partially ordered metric spaces. The obtained
results extend, complement and unify some recent coupled fixed point theorems
due to Samet [B. Samet, \textit{Coupled fixed point theorems for a generalized
Meir-Keeler contraction in partially ordered metric spaces}, Nonlinear Anal.
\textbf{72} (2010), 4508-4517], Bhaskar and Lakshmikantham [T.G. Bhaskar, V.
Lakshmikantham, \textit{Fixed point theorems in partially ordered metric spaces
and applications}, Nonlinear Anal. TMA \textbf{65} (2006) 1379-1393] and some
other very recent papers. An example to show that our generalizations are
effective is also presented
Coupled fixed point theorems for -contractive mixed monotone mappings in partially ordered metric spaces
In this paper we extend the coupled fixed point theorems for mixed monotone
operators obtained in [T.G. Bhaskar, V.
Lakshmikantham, \textit{Fixed point theorems in partially ordered metric spaces
and applications}, Nonlinear Anal. \textbf{65} (2006) 1379-1393] and [N.V.
Luong and N.X. Thuan, \textit{Coupled fixed points in partially ordered metric
spaces and application}, Nonlinear Anal. \textbf{74} (2011) 983-992], by
weakening the involved contractive condition. An example as well an application
to nonlinear Fredholm integral equations are also given in order to illustrate
the effectiveness of our generalizations
Common coupled fixed point theorems in -algebra-valued metric spaces
In this paper, we prove some common coupled fixed point theorems for mappings
satisfying different contractive conditions in the context of complete
-algebra-valued metric spaces. Moreover, the paper provides an application
to prove the existence and uniqueness of a solution for Fredholm nonlinear
integral equations.Comment: 12 pages. arXiv admin note: text overlap with arXiv:1506.05545 by
other author
Coupled coincidence point theorems for nonlinear contractions in partially ordered metric spaces
We obtain coupled coincidence and coupled common fixed point theorems for
mixed -monotone nonlinear operators in
partially ordered metric spaces. Our results are generalizations of recent
coincidence point theorems due to Lakshmikantham and \' Ciri\' c
[Lakshmikantham, V., \' Ciri\' c, L., \textit{Coupled fixed point theorems for
nonlinear contractions in partially ordered metric spaces}, Nonlinear Anal.
\textbf{70} (2009), 4341-4349], of coupled fixed point theorems established by
Bhaskar and Lakshmikantham [T.G. Bhaskar, V. Lakshmikantham, \textit{Fixed
point theorems in partially ordered metric spaces and applications}, Nonlinear
Anal. \textbf{65} (2006) 1379-1393] and also include as particular cases
several related results in very recent literature
Coincidence and Common Fixed Point Results for Generalized - Contractive Type Mappings with Applications
A new, simple and unified approach in the theory of contractive mappings was
recently given by Samet \emph{et al.} (Nonlinear Anal. 75, 2012, 2154-2165) by
using the concepts of --contractive type mappings and
-admissible mappings in metric spaces. The purpose of this paper is to
present a new class of contractive pair of mappings called generalized
- contractive pair of mappings and study various fixed point
theorems for such mappings in complete metric spaces. For this, we introduce a
new notion of -admissible w.r.t mapping which in turn generalizes
the concept of -monotone mapping recently introduced by
iri et al. (Fixed Point Theory Appl. 2008(2008), Article
ID 131294, 11 pages). As an application of our main results, we further
establish common fixed point theorems for metric spaces endowed with a partial
order as well as in respect of cyclic contractive mappings. The presented
theorems extend and subsumes various known comparable results from the current
literature. Some illustrative examples are provided to demonstrate the main
results and to show the genuineness of our results
Coupled Fixed Point Theorems for Contraction Involving Rational Expressions in Partially Ordered Metric Spaces
We establish coupled fixed point theorems for contraction involving rational
expressions in partially ordered metric spaces.Comment: Submitte
Nieto-Lopez theorems in ordered metric spaces
The comparison type version of the fixed point result in ordered metric
spaces established by Nieto and Rodriguez-Lopez [Acta Math. Sinica (English
Series), 23 (2007), 2205-2212] is nothing but a particular case of the
classical Banach's contraction principle [Fund. Math., 3 (1922), 133-181]
Generalized coupled fixed point theorems for mixed monotone mappings in partially ordered metric spaces
In this paper we extend the coupled fixed point theorems for mixed monotone
operators obtained in [T.G. Bhaskar, V.
Lakshmikantham, \textit{Fixed point theorems in partially ordered metric spaces
and applications}, Nonlinear Anal. TMA \textbf{65} (2006) 1379-1393] by
significantly weakening the involved contractive condition. Our technique of
proof is essentially different and more natural. An example as well an
application to periodic BVP are also given in order to illustrate the
effectiveness of our generalizations
Fixed point theorems for weak contraction in partially ordered G-metric space
In this article, we present some fixed point theorems in partially ordered
G-metric space using the concept of - weak contraction which
extend many existing fixed point theorems in such space. We also give some
examples to show that if we transform a metric space into a G-metric space our
results are not equivalent to the existing results in metric space
On n-tuplet fixed points for noncompact multivalued mappings via measure of noncompactness
In this paper, some results on the existence of n-tuplet fixed points for
multi-valued contraction mappings are proved via measure of noncompactness. As
an application, the existence of solutions for a system of integral inclusions
is studied.Comment: 13 page
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