On a theorem of Brian Fisher in the framework of w-distance

2017 ◽  
Vol 33 (2) ◽  
pp. 199-205
Author(s):  
DARKO KOCEV ◽  
◽  
VLADIMIR RAKOCEVIC ◽  
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Complete Metric Space ◽  
Point Theory ◽  
Common Fixed Points ◽  
Complete Metric Spaces ◽  
Condition C ◽  
Relaxing Condition

In 1980. Fisher in [Fisher, B., Results on common fixed points on complete metric spaces, Glasgow Math. J., 21 (1980), 165–167] proved very interesting fixed point result for the pair of maps. In 1996. Kada, Suzuki and Takahashi introduced and studied the concept of w–distance in fixed point theory. In this paper, we generalize Fisher’s result for pair of mappings on metric space to complete metric space with w–distance. The obtained results do not require the continuity of maps, but more relaxing condition (C; k). As a corollary we obtain a result of Chatterjea.

scholarly journals Two Fixed Point Theorems Concerning F-Contraction in Complete Metric Spaces

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 58 ◽  
Author(s):  
Ovidiu Popescu ◽  
Gabriel Stan
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Complete Metric Space ◽  
Point Theory ◽  
The Self ◽  
Complete Metric Spaces

In this paper, we generalize some results of Wardowski (Fixed Point Theory Appl. 2012:94, 2012), Cosentino and Vetro (Filomat 28:4, 2014), and Piri and Kumam (Fixed Point Theory Appl. 2014:210, 2014) theories by applying some weaker symmetrical conditions on the self map of a complete metric space and on the mapping F, concerning the contractions defined by Wardowski.

scholarly journals Fixed Point Theory inα-Complete Metric Spaces with Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
N. Hussain ◽  
M. A. Kutbi ◽  
P. Salimi
Keyword(s):  
Fixed Point ◽  
Continuous Function ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Complete Metric Space ◽  
Point Theory ◽  
Complete Metric Spaces ◽  
New Concepts ◽  
Rational Contraction

The aim of this paper is to introduce new concepts ofα-η-complete metric space andα-η-continuous function and establish fixed point results for modifiedα-η-ψ-rational contraction mappings inα-η-complete metric spaces. As an application, we derive some Suzuki type fixed point theorems and new fixed point theorems forψ-graphic-rational contractions. Moreover, some examples and an application to integral equations are given here to illustrate the usability of the obtained results.

scholarly journals Applications of Fixed Point Theory in Integral Equations and Homotopy Using Partially Ordered S_b Metric Spaces

2018 ◽  
Vol 7 (3.3) ◽  
pp. 146 ◽  
Author(s):  
D Ram Prasad ◽  
GNV Kishore ◽  
K Priyanka
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Homotopy Theory ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Complete Metric Space ◽  
Point Theory ◽  
Partially Ordered

In this paper we give some applications to integral equations as well as homotopy theory via Suzuki  type fixed point theorems in partially ordered complete  - metric space by using generalized contractive conditions. We also furnish an example which supports our main result.  

scholarly journals Semicompatibility and fixed point theorems in an unboundedD-metric space

2005 ◽  
Vol 2005 (5) ◽  
pp. 789-801
Author(s):  
Bijendra Singh ◽  
Shishir Jain ◽  
Shobha Jain
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contractive Condition ◽  
Restricted Domain

Rhoades (1996) proved a fixed point theorem in a boundedD-metric space for a contractive self-map with applications. Here we establish a more general fixed point theorem in an unboundedD-metric space, for two self-maps satisfying a general contractive condition with a restricted domain ofxandy. This has been done by using the notion of semicompatible maps inD-metric space. These results generalize and improve the results of Rhoades (1996), Dhage et al. (2000), and Veerapandi and Rao (1996). These results also underline the necessity and importance of semicompatibility in fixed point theory ofD-metric spaces. All the results of this paper are new.

EXISTENCE OF SOLUTION FOR A VOLTERRA TYPE INTEGRAL EQUATION USING DARBO-TYPE F-CONTRACTION

2021 ◽  
Vol 10 (6) ◽  
pp. 2687-2710
Author(s):  
F. Akutsah ◽  
A. A. Mebawondu ◽  
O. K. Narain
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Existence Of Solution ◽  
Volterra Type ◽  
Complete Metric Spaces ◽  
Type Integral ◽  
New Type

In this paper, we provide some generalizations of the Darbo's fixed point theorem and further develop the notion of $F$-contraction introduced by Wardowski in (\cite{wad}, D. Wardowski, \emph{Fixed points of a new type of contractive mappings in complete metric spaces,} Fixed Point Theory and Appl., 94, (2012)). To achieve this, we introduce the notion of Darbo-type $F$-contraction, cyclic $(\alpha,\beta)$-admissible operator and we also establish some fixed point and common fixed point results for this class of mappings in the framework of Banach spaces. In addition, we apply our fixed point results to establish the existence of solution to a Volterra type integral equation.

scholarly journals Fixed Points of g-Interpolative Ćirić–Reich–Rus-Type Contractions in b-Metric Spaces

Axioms ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 132
Author(s):  
Youssef Errai ◽  
El Miloudi Marhrani ◽  
Mohamed Aamri
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
New Type ◽  
The Given ◽  
Type Contraction

We use interpolation to obtain a common fixed point result for a new type of Ćirić–Reich–Rus-type contraction mappings in metric space. We also introduce a new concept of g-interpolative Ćirić–Reich–Rus-type contractions in b-metric spaces, and we prove some fixed point results for such mappings. Our results extend and improve some results on the fixed point theory in the literature. We also give some examples to illustrate the given results.

scholarly journals Coincidences and fixed points of reciprocally continuous and compatible hybrid maps

2002 ◽  
Vol 30 (10) ◽  
pp. 627-635 ◽  
Author(s):  
S. L. Singh ◽  
S. N. Mishra
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Multivalued Maps

It is proved that a pair of reciprocally continuous and nonvacuously compatible single-valued and multivalued maps on a metric space possesses a coincidence. Besides addressing two historical problems in fixed point theory, this result is applied to obtain new general coincidence and fixed point theorems for single-valued and multivalued maps on metric spaces under tight minimal conditions.

scholarly journals Coupled Coincidence Point Theorems for New Types of Mixed Monotone Multivalued Mappings in Partially Ordered Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Chalongchai Klanarong ◽  
Suthep Suantai
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Coupled Fixed Point ◽  
Point Theory ◽  
Multivalued Mappings ◽  
Complete Metric Spaces ◽  
Partially Ordered ◽  
Coupled Common Fixed Point ◽  
Recent Developments

We introduce and study new types of mixed monotone multivalued mappings in partially ordered complete metric spaces. We give relationships between those two types of mappings and prove their coupled fixed point and coupled common fixed point theorems in partially ordered complete metric spaces. Some examples of each type of mappings satisfying the conditions of the main theorems are also given. Our main result includes several recent developments in fixed point theory of mixed monotone multivalued mappings.

scholarly journals On coincidence and common fixed point theorems of eight self-maps satisfying an FM-contraction condition

2019 ◽  
Vol 24 (6) ◽  
Author(s):  
Mi Zhou ◽  
Xiao-Lan Liu ◽  
Adrian Secelean
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Common Property ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Complete Metric Spaces ◽  
Contraction Condition ◽  
New Type ◽  
The One

In this paper, a new type of contraction for several self-mappings of a metric space, called FM-contraction, is introduced. This extends the one presented for a single map by Wardowski [Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012:94, 2012]. Coincidence and common fixed point of eight self mappings satisfying FM-contraction conditions are established via common limit range property without exploiting the completeness of the space or the continuity of the involved maps. Coincidence and common fixed point of eight self-maps satisfying FM-contraction conditions via the common property (E.A.) are also studied. Our results generalize, extend and improve the analogous recent results in the literature, and some examples are presented to justify the validity of our main results.

scholarly journals Multi-valued F-contractions and the solutions of certain functional and integral equations

Filomat ◽  
2013 ◽  
Vol 27 (7) ◽  
pp. 1259-1268 ◽  
Author(s):  
Margherita Sgroi ◽  
Calogero Vetro
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contractive Condition ◽  
Ordered Metric Spaces ◽  
Complete Metric Spaces ◽  
Banach Contraction

Wardowski [Fixed Point Theory Appl., 2012:94] introduced a new concept of contraction and proved a fixed point theorem which generalizes Banach contraction principle. Following this direction of research, we will present some fixed point results for closed multi-valued F-contractions or multi-valued mappings which satisfy an F-contractive condition of Hardy-Rogers-type, in the setting of complete metric spaces or complete ordered metric spaces. An example and two applications, for the solution of certain functional and integral equations, are given to illustrate the usability of the obtained results.

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