scholarly journals Approximation fixed theorems for α-partial weakly Zamfirescu mappings with application to homotopy invariance

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1941-1956
Author(s):  
Aphinat Ninsri ◽  
Wutiphol Sintunavarat
Keyword(s):  
Fixed Point ◽  
Binary Relation ◽  
Metric Space ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Homotopy Invariance ◽  
Complete Metric Spaces ◽  
Approximate Fixed Point

In this paper, we introduce the concept of ?-partial weakly Zamfirescu mappings and give some approximate fixed point results for this mapping in ?-complete metric spaces. We also give some approximate fixed point results in ?-complete metric space endowed with an arbitrary binary relation and approximate fixed point results in ?-complete metric space endowed with graph. As application, we give homotopy results for ?-partial weakly Zamfirescu mapping.

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.

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.

scholarly journals Best Proximity Point for Generalized Proximal Weak Contractions in Complete Metric Space

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Erdal Karapınar ◽  
V. Pragadeeswarar ◽  
M. Marudai
Keyword(s):  
Approximate Solution ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Complete Metric Space ◽  
Optimal Approximate Solution ◽  
Weak Contraction ◽  
Complete Metric Spaces ◽  
New Class

We introduce a new class of nonself-mappings, generalized proximal weak contraction mappings, and prove the existence and uniqueness of best proximity point for such mappings in the context of complete metric spaces. Moreover, we state an algorithm to determine such an optimal approximate solution designed as a best proximity point. We establish also an example to illustrate our main results. Our result provides an extension of the related results in the literature.

scholarly journals Suzuki ψF-contractions and some fixed point results

2018 ◽  
Vol 34 (1) ◽  
pp. 93-102
Author(s):  
NICOLAE-ADRIAN SECELEAN ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Continuity Point ◽  
Picard Operator ◽  
Nonlinear Anal ◽  
New Type

The purpose of this paper is to combine and extend some recent fixed point results of Suzuki, T., [A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 (2009), 5313–5317] and Secelean, N. A. & Wardowski, D., [ψF-contractions: not necessarily nonexpansive Picard operators, Results Math., 70 (2016), 415–431]. The continuity and the completeness conditions are replaced by orbitally continuity and orbitally completeness respectively. It is given an illustrative example of a Picard operator on a non complete metric space which is neither nonexpansive nor expansive and has a unique continuity point.

scholarly journals Relation Theoretic (Θ,R) Contraction Results with Applications to Nonlinear Matrix Equations

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 767 ◽  
Author(s):  
Hamed Al-Sulami ◽  
Jamshaid Ahmad ◽  
Nawab Hussain ◽  
Abdul Latif
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Binary Relation ◽  
Metric Spaces ◽  
Matrix Equations ◽  
Existence Of A Solution ◽  
Complete Metric Spaces ◽  
Numerical Example ◽  
Nonlinear Matrix

Using the concept of binary relation R , we initiate a notion of Θ R -contraction and obtain some fixed point results for such mappings in the setting of complete metric spaces. Furthermore, we establish some new results of fixed points of N-order. Consequently, we improve and generalize the corresponding known fixed point results. As an application of our main result, we provide the existence of a solution for a class of nonlinear matrix equations. A numerical example is also presented to illustrate the theoretical findings.

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 Some Fixed Point Theorems Via Combination of Weak Contraction and Caristi Contractive Mapping

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Kushal Roy ◽  
Sayantan Panja ◽  
Mantu Saha ◽  
Zoran D. Mitrović
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Weak Contraction ◽  
Complete Metric Spaces ◽  
Contractive Mappings

Abstract In this paper we introduce some new types of contractive mappings by combining Caristi contraction, Ćirić-quasi contraction and weak contraction in the framework of a metric space. We prove some fixed point theorems for such type of mappings over complete metric spaces with the help of φ-diminishing property. Some examples are given in strengthening the hypothesis of our established theorems.

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