scholarly journals Some Remarks on Fixed Point Theorems for Interpolative Kannan Contraction

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Youssef Errai ◽  
El Miloudi Marhrani ◽  
Mohamed Aamri
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contraction Mappings ◽  
New Type ◽  
The Given ◽  
Kannan Contraction

In this paper, we use interpolation to obtain fixedpoint and common fixed point results for a new type of Kannan contraction mappings in complete metric and b -metric spaces. Our results extend and improve some results on fixed point theory in the literature. We also give some examples to illustrate the given results.

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 Some Common Fixed-Point Theorems for Generalized-Contractive-Type Mappings on Complex-Valued Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Chakkrid Klin-eam ◽  
Cholatis Suanoom
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contractive Type ◽  
Complex Valued ◽  
Common Fixed Point Theorems

Fixed-point theory in complex valued metric spaces has greatly developed in recent times. In this paper, we prove certain common fixed-point theorems for two single-valued mappings in such spaces. The mappings we consider here are assumed to satisfy certain metric inequalities with generalized fixed-point theorems due to Rouzkard and Imdad (2012). This extends and subsumes many results of other authors which were obtained for mappings on complex-valued metric spaces.

scholarly journals Common Fixed Point Theorems for Generalized Cyclic Contraction Pair in Partial B-Metric Spaces

2019 ◽  
Vol 8 (10S) ◽  
pp. 85-89
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Cyclic Contraction ◽  
Common Fixed Point Theorems

In this paper, we introduce the notion of generalized cyclic contraction pair with transitive mapping in partial b-metric spaces. Also, we establish some fixed point theorems for this contraction pair. Our results generalize and improve the result of Oratai Yamaod, Wutiphol Sintunavarat and Yeol Je Cho (Fixed Point Theory App. 2015:164) in partial-b-metric spaces.

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 Ciric contractions on metric spaces with applications

Filomat ◽  
2014 ◽  
Vol 28 (9) ◽  
pp. 1953-1964 ◽  
Author(s):  
N. Hussain ◽  
N. Yasmin ◽  
N. Shafqat
Keyword(s):  
Fixed Point ◽  
Nonlinear Analysis ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contractive Maps

In this paper, using the concept of w-distance, we obtain fixed point results for multi-valued generalized w-contractive maps not involving the extended Hausdorf metric. Presented theorems are generalizations of recent fixed point theorems due to L.B. Cric [Nonlinear Analysis 71 (2009), 2716-2723], D. Klim and D. Wardowski [ J. Math. Anal. Appl. 334 (2007), 132-139], Y. Feng and S. Liu [J. Math. Anal. Appl. 317 (2006), 103-112], Latif and Abdou [Nonlinear Analysis 74 (2011), 1436-1444 and Fixed Point Theory and Appl., Volume 2009 (2009) Article ID 487161, 8 pp.] and several others. As an application of our results we establish common fixed point results for newly defined class of Banach operator pairs.

Two new types of fixed point theorems for F-contraction

2016 ◽  
Vol 7 (4) ◽  
pp. 251 ◽  
Author(s):  
Sami Khan ◽  
Muhammad Arshad ◽  
Aftab Hussain ◽  
Muhammad Nazam
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contraction Principle ◽  
Complete Metric Spaces ◽  
New Type

The purpose of the present paper is to continue the study of fixed pointtheory in complete metric spaces. Wardowski [Fixed Point Theory Appl. 2012: 94]introduced a new type of contraction called \(F\)-contraction and proved afixed point result in complete metric spaces, which in turn generalize theBanach contraction principle. The aim of this paper is to extend the conceptof $F$-contraction into generalized \(F\)-contraction. An example andapplication are given to illustrate the usability of the 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.

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