scholarly journals Coupled fixed point theorems in complete metric spaces endowed with a directed graph and application

2017 ◽  
Vol 15 (1) ◽  
pp. 734-744 ◽  
Author(s):  
Mehmet Kir ◽  
Esra Yolacan ◽  
Hukmi Kiziltunc
Keyword(s):  
Fixed Point ◽  
Directed Graph ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Monotone Operators ◽  
Existence Results ◽  
Contractive Condition ◽  
Complete Metric Spaces ◽  
Mixed Monotone Operators

Abstract The purpose of this paper is to present some existence results for coupled fixed point of a (φ,ψ) —contractive condition for mixed monotone operators in metric spaces endowed with a directed graph. Our results generalize the results obtained by Jain et al. in (International Journal of Analysis, Volume 2014, Article ID 586096, 9 pages). Moreover, we have an application to some integral system to support the results.

Some Common Fixed Point Theorem in Complete Metric Space of Integral Type

2018 ◽  
Vol 6 (8) ◽  
pp. 297
Author(s):  
Jagdish C. Chaudhary ◽  
Shailesh T. Patel
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Contractive Condition ◽  
Integral Type ◽  
Complete Metric Spaces ◽  
Common Fixed Point Theorems ◽  
Common Fixed Point Theorem

In this paper, we prove some common fixed point theorems in complete metric spaces for self mapping satisfying a contractive condition of Integral  type.

A generalization of Reich’s fixed point theorem for multi-valued mappings

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3295-3305 ◽  
Author(s):  
Antonella Nastasi ◽  
Pasquale Vetro
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Complete Metric Spaces ◽  
New Class ◽  
Banach Contraction ◽  
The Banach Contraction Principle

Motivated by a problem concerning multi-valued mappings posed by Reich [S. Reich, Some fixed point problems, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 57 (1974) 194-198] and a paper of Jleli and Samet [M. Jleli, B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl. 2014:38 (2014) 1-8], we consider a new class of multi-valued mappings that satisfy a ?-contractive condition in complete metric spaces and prove some fixed point theorems. These results generalize Reich?s and Mizoguchi-Takahashi?s fixed point theorems. Some examples are given to show the usability of the obtained results.

scholarly journals Some fixed point theorems via partial order relations without the monotone property

2015 ◽  
Vol 31 (3) ◽  
pp. 389-394
Author(s):  
WARUT SAKSIRIKUN ◽  
◽  
NARIN PETROT ◽  
Keyword(s):  
Fixed Point ◽  
Partial Order ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Order Relation ◽  
Monotone Mappings ◽  
Complete Metric Spaces ◽  
Nonlinear Anal ◽  
Monotonic Properties

The main aim of this paper is to consider some fixed point theorems via a partial order relation in complete metric spaces, when the considered mapping may not satisfy the monotonic properties. Furthermore, we also obtain some couple fixed point theorems, which can be viewed as an extension of a result that was presented in [V. Berinde, Generalized coupled fixed point theorems for mixed monotone mappings in partially ordered metric spaces, Nonlinear Anal., 74 (2011), 7347–7355].

scholarly journals Coupled Fixed-Point Theorems for Contractions in Partially Ordered Metric Spaces and Applications

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
M. Eshaghi Gordji ◽  
Y. J. Cho ◽  
S. Ghods ◽  
M. Ghods ◽  
M. Hadian Dehkordi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Contractive Condition ◽  
Coincidence Points ◽  
Ordered Metric Spaces ◽  
Coupled Coincidence Points ◽  
Definition Of ◽  
Coupled Coincidence

Bhaskar and Lakshmikantham (2006) showed the existence of coupled coincidence points of a mappingFfromX×XintoXand a mappinggfromXintoXwith some applications. The aim of this paper is to extend the results of Bhaskar and Lakshmikantham and improve the recent fixed-point theorems due to Bessem Samet (2010). Indeed, we introduce the definition of generalizedg-Meir-Keeler type contractions and prove some coupled fixed point theorems under a generalizedg-Meir-Keeler-contractive condition. Also, some applications of the main results in this paper are given.

scholarly journals A constructive approach to coupled fixed point theorems in metric spaces

2015 ◽  
Vol 31 (3) ◽  
pp. 277-287
Author(s):  
VASILE BERINDE ◽  
◽  
MADALINA PACURAR ◽  
◽  
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Iterative Methods ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Contractive Condition ◽  
Constructive Approach ◽  
New Type

In this paper we establish the existence and uniqueness of a coupled fixed point for operators F : X × X → X satisfying a new type of contractive condition, which is weaker than all the corresponding ones studied in literature so far. We also provide constructive features to our coupled fixed point results by proving that the unique coupled fixed point of F can be approximated by means of two distinct iterative methods: a Picard type iterative method of the form xn+1 = F(xn, xn), n ≥ 0, with x0 ∈ X, as well as a two step iterative method of the form yn+1 = F(yn−1, yn), n ≥ 0, with y0, y1 ∈ X. We also give appropriate error estimates for both iterative methods. Essentially we point out that all coupled fixed point theorems existing in literature, that establish the existence and uniqueness of a coupled fixed point with equal components, could be derived in a much more simpler manner.

scholarly journals Endpoints of multi-valued weakly contraction in complete metric spaces endowed with graphs

Filomat ◽  
2017 ◽  
Vol 31 (14) ◽  
pp. 4319-4329 ◽  
Author(s):  
Jukrapong Tiammee ◽  
Suthep Suantai
Keyword(s):  
Fixed Point ◽  
Directed Graph ◽  
Metric Space ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Sufficient Conditions ◽  
Ordered Metric Spaces ◽  
Partially Ordered Metric Spaces ◽  
Complete Metric Spaces ◽  
Partially Ordered

In this paper, we introduce a new concept of weak G-contraction for multi-valued mappings on a metric space endowed with a directed graph. Endpoint theorem of this mapping is established under some sufficient conditions in a complete metric space endowed with a directed graph. Our main results extend and generalize those fixed point in partially ordered metric spaces. Some examples supporting our main results are also given. Moreover, we apply our main results to obtain some coupled fixed point results in the context of complete metric spaces endowed with a directed graph which are more general than those in partially ordered metric spaces.

scholarly journals Fixed points results via simulation functions

Filomat ◽  
2016 ◽  
Vol 30 (8) ◽  
pp. 2343-2350 ◽  
Author(s):  
Erdal Karapınar
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Simulation Function ◽  
Complete Metric Spaces ◽  
Admissible Mapping ◽  
Simulation Functions

In this paper, we present some fixed point results in the setting of a complete metric spaces by defining a new contractive condition via admissible mapping imbedded in simulation function. Our results generalize and unify several fixed point theorems in the literature.

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