scholarly journals Orbital continuity and fixed points

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3495-3499 ◽  
Author(s):  
Abhijit Pant ◽  
R.P. Pant
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Space ◽  
Complete Metric Space ◽  
Sufficient Condition ◽  
Point Property ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
Type Contraction

The aim of the present paper is to show the significance of the concept of orbital continuity introduced by Ciric. We prove that orbital continuity of a pair of R-weak commuting self-mappings of type Af or of type A1 of a complete metric space is equivalent to fixed point property under Jungck type contraction. We also establish a situation in which orbital continuity is a necessary and sufficient condition for the existence of a common fixed point of a pair of mappings yet the mappings are necessarily discontinuous at the fixed point.

scholarly journals Necessary and sufficient conditions for common fixed point theorems in fuzzy metric space

2009 ◽  
Vol 42 (4) ◽  
Author(s):  
D. O’Regan ◽  
M. Abbas
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Sufficient Conditions ◽  
Fuzzy Metric Space ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
Common Fixed Point Theorems

AbstractThe aim of this paper is to provide a necessary and sufficient condition for the existence of a common fixed point of three maps

scholarly journals A remark on asymptotic regularity and fixed point property

Filomat ◽  
2019 ◽  
Vol 33 (14) ◽  
pp. 4665-4671
Author(s):  
Ravindra Bisht
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Complete Metric Space ◽  
Fixed Point Property ◽  
Point Property ◽  
Necessary And Sufficient Condition ◽  
Asymptotic Regularity ◽  
The Common ◽  
Necessary And Sufficient ◽  
Commuting Mappings

In this paper, we show that orbital continuity of a pair of non-commuting mappings of a complete metric space is equivalent to fixed point property under the Proinov type condition. Furthermore, we establish a situation in which orbital continuity turns out to be a necessary and sufficient condition for the existence of a common fixed point of a pair of mappings yet the mappings are not necessarily continuous at the common fixed point.

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 Necessary and sufficient fixed point critera involving attractors

1993 ◽  
Vol 48 (1) ◽  
pp. 109-116
Author(s):  
Jacek Jachymski
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Complete Metric Space ◽  
Positive Real ◽  
Necessary And Sufficient ◽  
Equivalent Conditions

Let f be a continuous self-map on a complete metric space X and p ∈ X. Let c be a positive real. Equivalent conditions are given for the singleton {p} to be an attractor of a set of c−fixed points of f. We also establish equivalent conditions for the existence of a contractive fixed point of f. These results subsume a body of fixed point theorems.

scholarly journals Interpolative Reich–Rus–Ćirić and Hardy–Rogers Contraction on Quasi-Partial b-Metric Space and Related Fixed Point Results

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1598 ◽  
Author(s):  
Vishnu Narayan Mishra ◽  
Luis Manuel Sánchez Ruiz ◽  
Pragati Gautam ◽  
Swapnil Verma
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Metric Space ◽  
Complete Metric Space ◽  
Contraction Condition ◽  
Common Fixed Point Theorem ◽  
Type Contraction

The aim of this paper was to obtain common fixed point results by using an interpolative contraction condition given by Karapinar in the setting of complete metric space. Here in this paper, we have redefined the Reich–Rus–Ćirić type contraction and Hardy–Rogers type contraction in the framework of quasi-partial b-metric space and proved the corresponding common fixed point theorem by adopting the notion of interpolation. The results are further validated with the application based on them.

On common fixed points for a family of mappings

1975 ◽  
Vol 13 (2) ◽  
pp. 261-267 ◽  
Author(s):  
S.A. Husain ◽  
V.M. Sehgal
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Complete Metric Space ◽  
Common Fixed Points ◽  
Common Fixed Point Theorems

The purpose of this paper is to obtain some common fixed point theorems for a family of mappings in a complete metric space. The results herein improve some of the recent theorems of Kiyoshi Iséki (Bull. Austral. Math. Soc. 10 (1974), 365–370).

scholarly journals Common Fixed Points of Compatible Mappings

2012 ◽  
Vol 4 (3) ◽  
pp. 603-608
Author(s):  
M. P. Singh ◽  
R. Yumnam
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Complete Metric Space ◽  
Common Fixed Points ◽  
Compatible Mappings ◽  
Type B ◽  
Common Fixed Point Theorems

In this paper we prove two common fixed point theorems by considering four mappings in complete metric space. In the first theorem we consider two pairs of compatible mappings of type (A) and in the second theorem we consider two pairs of compatible mappings of type (B). Our results modify and extend some earlier results in the literature.© 2012 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.doi: http://dx.doi.org/10.3329/jsr.v4i3.10567 J. Sci. Res. 4 (3), 603-608 (2012)

scholarly journals Common fixed points of two nonexpansive mappings in Banach spaces

2004 ◽  
Vol 69 (1) ◽  
pp. 1-18 ◽  
Author(s):  
Tomonari Suzuki
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Convergence Theorem ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

In this paper, we discuss a necessary and sufficient condition for common fixed points of two nonexpansive mappings. We then prove a convergence theorem to a common fixed point. Finally, we discuss the existence of a nonexpansive retraction onto the set of common fixed points of nonexpansive mappings. In these theorems, we do not assume the strict (uniform) convexity of the norm of the Banach space.

Fixed point theorems for expansive mappings in Gp-metric spaces

2017 ◽  
Vol 26 (3) ◽  
pp. 297-308
Author(s):  
MELTEM KAYA ◽  
◽  
HASAN FURKAN ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partial Metric ◽  
Expansive Mapping ◽  
Partial Metric Spaces ◽  
Weak Compatibility

In the present paper, we adopt the concept of expansive mapping in the context of Gp-metric spaces in a similar manner expansive mapping in metric spaces. Furthermore, we obtain some results on fixed points of expansive type mappings. Also, we prove some common fixed point results for expansive mappings by using the notion of weak compatibility in Gp-metric space. Our results generalize some comparable results in metric spaces and partial metric spaces to Gp-metric spaces. Moreover, some examples are introduced in order to support our new results.

scholarly journals Common Fixed Point for Generalized Bose-Mukherjee-Type Fuzzy Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Ming-liang Song ◽  
Zhong-qian Wang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Metric Space ◽  
Complete Metric Space ◽  
Common Fixed Point Theorem

We prove a common fixed point theorem for a pair of generalized Bose-Mukherjee-type fuzzy mappings in a complete metric space. An example is also provided to support the main result presented herein.

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