A Fixed Point Theorem for Weakly Uniformly Strict Contractions(1)

1973 ◽  
Vol 16 (1) ◽  
pp. 15-18 ◽  
Author(s):  
Nadim A. Assad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Complete Metric Space ◽  
Strict Contraction ◽  
Image Position

In Meir and Keeler [3], the authors proved a fixed point theorem in a complete metric space (X, d) for a mapping f that satisfies the following condition of weakly uniformly strict contraction:Given ∊ > 0, there exists δ > 0 such that(A)

scholarly journals A fixed point theorem with applications to convolution equations

1963 ◽  
Vol 3 (4) ◽  
pp. 385-395 ◽  
Author(s):  
R. E. Edwards
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Unique Fixed Point ◽  
Complete Metric Space ◽  
Banach Contraction Principle ◽  
Banach Contraction ◽  
Image Position ◽  
Convolution Equations

The well-known Banach Contraction Principle asserts that any self-map F of a complete metric space M with the property that, for some number k < 1, for all x, y,∈M, possesses a unique fixed point in M. some extensions and analogues have recently been given by Edelstein [1]. For the reader's convenlience we state here the result of Edelstein which we shall employ. It asserts that if F is a self-map of a metric space M having the property that for any two distinct points x and y of M, and if x0 is a point of M such that the sequence of iterates xn = Fn (x0) contains a subsequence which converges in M, then the limit of this subsequence is the unique fixed point of F.

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.

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.

A Common Fixed Point Theorem Connected to a Result of V. Popa and H. K. Pathak

2006 ◽  
Vol 13 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Mohamed Akkouchi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Metric Space ◽  
Complete Metric Space ◽  
Weakly Compatible ◽  
Common Fixed Point Theorem

Abstract In this paper, we prove a common fixed point theorem for two pairs of weakly compatible self-mappings of a complete metric space without requiring continuity. Our result generalizes a theorem obtained by V. Popa and H. K. Pathak in 1998 and a result obtained by B. Fisher and S. Sessa in 1986.

scholarly journals On Pata–Suzuki-Type Contractions

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 720
Author(s):  
Obaid Alqahtani ◽  
Venigalla Madhulatha Himabindu ◽  
Erdal Karapınar
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Metric Space ◽  
Complete Metric Space ◽  
Admissible Mapping

In this paper, we aim to obtain fixed-point results by merging the interesting fixed-point theorem of Pata and Suzuki in the framework of complete metric space and to extend these results by involving admissible mapping. After introducing two new contractions, we investigate the existence of a (common) fixed point in these new settings. In addition, we shall consider an integral equation as an application of obtained results.

scholarly journals Weak Contraction Condition Involving Cubic Terms ofdx,yunder the Fixed Point Consideration

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Penumurthy Parvateesam Murthy ◽  
K. N. V. V. Vara Prasad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Complete Metric Space ◽  
Contractive Condition ◽  
Weak Contraction ◽  
Contraction Condition

A fixed point theorem is presented for single-valued map with using generalizedφ-weak contractive condition involving various combinations ofdx,yon a complete metric space. Our result is an extension as well as a generalization of Alber and Guerre-Delabriere (1997) in particular. It also generalizes the results of Rhoades (2001), Choudhury and Dutta, (2000), and Dutta and Choudhury, (2008).

scholarly journals A Fixed Point Theorem for Multivalued Mappings withδ-Distance

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Özlem Acar ◽  
Ishak Altun
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Complete Metric Space ◽  
Multivalued Mappings

We mainly study fixed point theorem for multivalued mappings withδ-distance using Wardowski’s technique on complete metric space. Let(X,d)be a metric space and letB(X)be a family of all nonempty bounded subsets ofX. Defineδ:B(X)×B(X)→Rbyδ(A,B)=supd(a,b):a∈A,b∈B.Consideringδ-distance, it is proved that if(X,d)is a complete metric space andT:X→B(X)is a multivalued certain contraction, thenThas a fixed point.

scholarly journals Some fixed point theorems for Hardy-Rogers type mappings

1984 ◽  
Vol 7 (1) ◽  
pp. 75-87 ◽  
Author(s):  
B. E. Rhoades ◽  
S. Sessa ◽  
M. S. Khan ◽  
M. D. Khan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Complete Metric Space ◽  
The Other

The first result establishes a fixed point theorem for three maps of a complete metric space. The contractive definition is a generalization of that of Hardy and Rogers, and the commuting condition of Jungck is replaced by the concept of weakly commuting. The other results are extensions of some theorems of Kannan.

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