scholarly journals Stability of tripled fixed point iteration procedures for mixed monotone mappings

2014 ◽  
Vol 6 (2) ◽  
pp. 377-388
Author(s):  
I. Timis
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Monotone Mappings ◽  
Cone Metric Spaces ◽  
Fixed Point Iteration ◽  
Tripled Fixed Point ◽  
Nonlinear Anal ◽  
Contractive Type ◽  
Definition Of ◽  
Stability Definition

Recently, Berinde and Borcut [Berinde, V. and Borcut, M., Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal. 74 (2011), 4889-4897] introduced the concept of tripled fixed point and by now, there are several researches on this subject, in partially metric spaces and in cone metric spaces. In this paper, we introduce the notion of stability definition of tripled fixed point iteration procedures and establish stability results for mixed monotone mappings which satisfy various contractive conditions. Our results extend and complete some existing results in the literature. An illustrative example is also given.

scholarly journals Some tripled coincidence point theorems for almost generalized contractions in ordered metric spaces

2012 ◽  
Vol 44 (3) ◽  
pp. 233-251 ◽  
Author(s):  
Erdal KARAPINAR ◽  
Hassen AYDI ◽  
Zead MUSTAFA
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Ordered Metric Spaces ◽  
Tripled Fixed Point ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered ◽  
Nonlinear Anal ◽  
Contractive Type ◽  
Common Fixed Point Theorems

In this paper, we prove tripledcoincidence and common fixed point theorems for $F: X\times X\times X\to X$ and $g:X\to X$ satisfying almost generalized contractions in partially ordered metric spaces. The presented results generalize the theorem of Berinde and Borcut Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal 74(15) (2011)4889--4897. Also, some examples are presented.

scholarly journals Exciting Fixed Point Results under a New Control Function with Supportive Application in Fuzzy Cone Metric Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2267
Author(s):  
Hasanen A. Hammad ◽  
Manuel De la De la Sen
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Control Function ◽  
Cone Metric Spaces ◽  
Tripled Fixed Point ◽  
Contractive Type ◽  
Theoretical Results ◽  
Cone Metric

The objective of this paper is to present a new notion of a tripled fixed point (TFP) findings by virtue of a control function in the framework of fuzzy cone metric spaces (FCM-spaces). This function is a continuous one-to-one self-map that is subsequentially convergent (SC) in FCM-spaces. Moreover, by using the triangular property of a FCM, some unique TFP results are shown under modified contractive-type conditions. Additionally, two examples are discussed to uplift our work. Ultimately, to examine and support the theoretical results, the existence and uniqueness solution to a system of Volterra integral equations (VIEs) are obtained.

scholarly journals Tripled fixed point theorems for monotone mappings in partially ordered metric spaces

2012 ◽  
Vol 28 (2) ◽  
pp. 215-222
Author(s):  
MARIN BORCUT ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Monotone Mappings ◽  
Ordered Metric Spaces ◽  
Tripled Fixed Point ◽  
Partially Ordered Metric Spaces ◽  
Complete Metric Spaces ◽  
Partially Ordered ◽  
Contractive Type

In this paper, we introduce the concept of tripled fixed point for nonlinear and monotone mappings in partially ordered complete metric spaces and obtain existence as well as existence and uniqueness theorems for contractive type mappings. Our results generalize and extend recent tripled fixed point theorems established by Berinde and Borcut [Berinde, V., Borcut, M., Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces. Nonlinear Anal. 74 (2011) 4889–4897]. Examples to support our new results are given.

scholarly journals Coupled fixed point theorems in partially ordered cone metric spaces

Filomat ◽  
2011 ◽  
Vol 25 (2) ◽  
pp. 137-149 ◽  
Author(s):  
Hui-Sheng Ding ◽  
Lu Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Monotone Mappings ◽  
Ordered Metric Space ◽  
Cone Metric Spaces ◽  
Partially Ordered ◽  
Nonlinear Anal ◽  
Cone Metric

This paper is concerned with mixed monotone mappings in partially ordered cone metric spaces. We establish several fixed point theorems, which generalize and complement some known results. Especially, even in a partially ordered metric space, our main results are generalizations of the fixed point theorems due to Bhaskar and Lakshmikantham [T. Grana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. TMA 65 (2006) 1379-1393].

scholarly journals Tripled coincidence theorems for monotone mappings in partially ordered metric spaces

2012 ◽  
Vol 21 (2) ◽  
pp. 135-142
Author(s):  
MARIN BORCUT ◽  
Keyword(s):  
Metric Spaces ◽  
Monotone Mappings ◽  
Contractive Condition ◽  
Ordered Metric Spaces ◽  
Tripled Fixed Point ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered ◽  
Nonlinear Anal ◽  
Coincidence Theorems ◽  
Contractive Type

In this paper, we establish tripled coincidence point theorems for a pair of mappings F : X × X × X → X and g : X → X satisfying a nonlinear contractive condition ordered metric spaces. Presented theorems extend several existing results in the literature: [Borcut, M. and Berinde, V., Tripled coincidente point theorems for contractive type mappings in partially ordered metric spaces, Aplied Mathematics and Computation, 218 (2012), No. 10, 5929–5936], and Berinde, Borcut in article [Berinde, V., Borcut, M., Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal., 74 (2011), 4889-4897].

scholarly journals Common fixed point theorems for generalized G- η-χ–contractive type mappings with applications

2017 ◽  
Vol 37 (1) ◽  
pp. 9-20
Author(s):  
Manoj Kumar ◽  
Serkan Araci
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Mappings ◽  
Nonlinear Anal ◽  
Contractive Type ◽  
Common Fixed Point Theorems

Samet et. al. (Nonlinear Anal. 75, 2012, 2154-2165) introduced the concept of alpha-psi-contractive type mappings in metric spaces. In 2013, Alghamdi et. al. [2] introduced the concept of G-β--contractive type mappings in G-metric spaces. Our aim is to introduce new concept of generalized G-η-χ-contractive pair of mappings. Further, we study some fixed point theorems for such mappings in complete G-metric spaces. As an application, we further establish common fixed point theorems for G-metric spaces for cyclic contractive mappings.

scholarly journals On Complete Cone Metric Space and Fixed Point Theorem

2011 ◽  
Vol 3 (2) ◽  
pp. 303-309
Author(s):  
J. Mehta ◽  
M. L. Joshi
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Cone Metric Space ◽  
Weakly Compatible Maps ◽  
Cone Metric Spaces ◽  
Weakly Compatible ◽  
Contractive Type ◽  
Cone Metric

We prove coincidence and common fixed point theorems of four self mappings satisfying a generalized contractive type condition in complete cone metric spaces. Our results generalize some well-known recent results.Keywords: Common fixed point; Complete cone metric space; Weakly compatible maps.© 2011 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.doi:10.3329/jsr.v3i2.6475                J. Sci. Res. 3 (2), 303-309 (2011)

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].

A new contribution in fuzzy cone metric spaces by strong fixed point techniques with supportive application

2021 ◽  
pp. 1-21
Author(s):  
Rashwan A. Rashwan ◽  
Hasanen A. Hammad ◽  
A. Nafea
Keyword(s):  
Fixed Point ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Mixed Monotone Property ◽  
Cone Metric Spaces ◽  
System Of Integral Equations ◽  
Tripled Fixed Point ◽  
Fixed Point Techniques ◽  
Theoretical Results ◽  
Cone Metric

In this manuscript, the concept of a cyclic tripled type fuzzy cone contraction mapping in the setting of fuzzy cone metric spaces is introduced. Also, some theoretical results concerned with tripled fixed points are given without a mixed monotone property in the mentioned space. Moreover, under this concept, some strong tripled fixed point results are obtained. Ultimately, to support the theoretical results non-trivial examples are listed and the existence of a unique solution to a system of integral equations is presented as an application.

Ulam-Hyers stability theorem by tripled fixed point theorem

2016 ◽  
Vol 56 (1) ◽  
pp. 77-97
Author(s):  
Animesh Gupta
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Stability Theorem ◽  
Tripled Fixed Point ◽  
Complete Metric Spaces ◽  
Contractive Type ◽  
Vector Valued ◽  
Stability Results

AbstractThis paper deals with tripled fixed point theorem, and the approach is based on Perov-type fixed point theorem for contractions in metric spaces endowed with vector-valued metrics. We are also study Ulam-Hyers stability results for the tripled fixed points of a triple of contractive type single-valued and respectively multi-valued operators on complete metric spaces.

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