scholarly journals A NOTE ON THE PAPER “ON COMPLETENESS IN METRIC SPACES AND FIXED POINT THEOREMS"

2020 ◽  
Vol 15 (1) ◽  
Author(s):  
Deepak Khantwal ◽  
Umesh Cuandra Gairola
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Continuous Mappings ◽  
Discontinuous Mappings ◽  
The Fixed Point Theorem ◽  
Common Fixed Point Theorem

In the present note, we show that the assumption of continuity used in the fixed point theorem of Gregori et al. (Results Math. 73 (2018), no. 4, Art. 142, 13) can be relaxed to some weaker version of continuity. More precisely, we prove a fixed point theorem for orbitally continuous and k-continuous mappings in weak G-complete metric space and provide an appropriate example to show that our result is not only valid for continuous mappings but also for some discontinuous mappings. Moreover, we apply our main result to establish a common fixed point theorem for two self-mappings

scholarly journals A common fixed point theorem for cyclic operators on partial metric spaces

Filomat ◽  
2012 ◽  
Vol 26 (2) ◽  
pp. 407-414 ◽  
Author(s):  
Erdal Karapınar ◽  
Nabi Shobkolaei ◽  
Shaban Sedghi ◽  
Mansour Vaezpour
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partial Metric ◽  
Partial Metric Spaces ◽  
Cyclic Operators ◽  
Common Fixed Point Theorem

In this paper, we prove a common fixed point theorem for two self-mappings satisfying certain conditions over the class of partial metric spaces. In particular, the main theorem of this manuscript extends some well-known fixed point theorems in the literature on this topic.

scholarly journals Common Fixed Point Theorems for a Rational Inequality in Complex Valued Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Pankaj Kumar ◽  
Manoj Kumar ◽  
Sanjay Kumar
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complex Valued ◽  
Common Fixed Point Theorems ◽  
Common Fixed Point Theorem

We prove a common fixed point theorem for a pair of mappings. Also, we prove a common fixed point theorem for pairs of self-mappings along with weakly commuting property.

scholarly journals Fixed Point Results of Expansive Mappings in Metric Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1800
Author(s):  
Seher Sultan Yeşilkaya ◽  
Cafer Aydın
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Compatible Mappings ◽  
Ordered Metric Spaces ◽  
Expansive Mapping ◽  
Weakly Compatible ◽  
Common Fixed Point Theorem

In this study, we introduce the concept of θ-expansive mapping in ordered metric spaces and prove a fixed point theorem for such mappings. We give some fixed point results for θ-expansive mapping in metric spaces and prove fixed point theorems for such mappings. These results extend the main results of many comparable results from the current literature. We also obtain a common fixed point theorem of two weakly compatible mappings in metric spaces. Finally, the examples are presented to support the new theorems and results proved.

scholarly journals Common Fixed Point Theorems of Altman Integral Type Mappings inG-Metric Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Feng Gu ◽  
Hongqing Ye
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Integral Type ◽  
Common Fixed Point Theorems ◽  
Common Fixed Point Theorem

We introduce the concept ofφ-weakly commuting self-mapping pairs inG-metric space. Using this concept, we establish a new common fixed point theorem of Altman integral type for six self-mappings in the framework of completeG-metric space. An example is provided to support our result. The results obtained in this paper differ from the recent relative results in the literature.

scholarly journals Common Fixed Point Theorems via Inverse C k − Class Functions in Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-25
Author(s):  
Mi Zhou ◽  
Xiao-Lan Liu ◽  
Arslan Hojat Ansari ◽  
Mukesh Kumar Jain ◽  
Jia Deng
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Common Fixed Point Theorems ◽  
Common Fixed Point Theorem

In this paper, we firstly introduce a new notion of inverse C k − class functions which extends the notion of inverse C − class functions introduced by Saleem et al., 2018. Secondly, some common fixed point theorems are stated under some compatible conditions such as weak semicompatible of type A , weak semicompatibility, and conditional semicompatibility in metric spaces. Moreover, we introduce a new kind of compatibility called S τ − compatibility which is weaker than E . A . property and also present a common fixed point theorem in metric spaces via inverse C k − class functions. Some examples are provided to support our results.

Fixed point theorems in generalized metric spaces

2016 ◽  
Vol 10 (02) ◽  
pp. 1750030
Author(s):  
Stefan Czerwik ◽  
Krzysztof Król
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Banach Fixed Point Theorem ◽  
Generalized Metric Space ◽  
Generalized Metric

In the paper, we shall prove the results on the existence of fixed points of mapping defined on generalized metric space satisfying a nonlinear contraction condition, which is a generalization of Diaz and Margolis theorem (see [A fixed point theorem of the alternative, for contractions on a generalized complete metric space, Bull. Amer. Math. Soc. 74 (1968) 305–309]). We also present local fixed point theorems both in generalized and ordinary metric spaces. Our results are generalizations of Banach fixed point theorem and many other 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 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.

Fixed point theorems for nonself Bianchini type contractions in Banach spaces endowed with a graph

2018 ◽  
Vol 27 (1) ◽  
pp. 37-48
Author(s):  
ANDREI HORVAT-MARC ◽  
◽  
LASZLO BALOG ◽  
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contraction Condition

In this paper we present an extension of fixed point theorem for self mappings on metric spaces endowed with a graph and which satisfies a Bianchini contraction condition. We establish conditions which ensure the existence of fixed point for a non-self Bianchini contractions T : K ⊂ X → X that satisfy Rothe’s boundary condition T (∂K) ⊂ K.

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