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 Fisher Fixed Point Results in Generalized Metric Spaces with a Graph

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Karim Chaira ◽  
Abderrahim Eladraoui ◽  
Mustapha Kabil ◽  
Abdessamad Kamouss
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Generalized Metric Space ◽  
Generalized Metric Spaces ◽  
Generalized Metric ◽  
Banach Contraction

We discuss Fisher’s fixed point theorem for mappings defined on a generalized metric space endowed with a graph. This work should be seen as a generalization of the classical Fisher fixed point theorem. It extends some recent works on the enlargement of Banach Contraction Principle to generalized metric spaces with graph. An example is given to illustrate our result.

scholarly journals Caristi Fixed Point Theorem in Metric Spaces with a Graph

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
M. R. Alfuraidan ◽  
M. A. Khamsi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Caristi’S Fixed Point Theorem ◽  
Banach Contraction ◽  
Caristi's Fixed Point Theorem

We discuss Caristi’s fixed point theorem for mappings defined on a metric space endowed with a graph. This work should be seen as a generalization of the classical Caristi’s fixed point theorem. It extends some recent works on the extension of Banach contraction principle to metric spaces with graph.

scholarly journals Fixed point theorem with contractive mapping on C*-Algebra valued G-Metric Space

2021 ◽  
Vol 2106 (1) ◽  
pp. 012015
Author(s):  
A Wijaya ◽  
N Hariadi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Unique Fixed Point ◽  
Complete Metric Space ◽  
Contractive Mapping ◽  
C Algebra ◽  
Metric Function ◽  
Interesting Theorem

Abstract Banach-Caccioppoli Fixed Point Theorem is an interesting theorem in metric space theory. This theorem states that if T : X → X is a contractive mapping on complete metric space, then T has a unique fixed point. In 2018, the notion of C *-algebra valued G-metric space was introduced by Congcong Shen, Lining Jiang, and Zhenhua Ma. The C *-algebra valued G-metric space is a generalization of the G-metric space and the C*-algebra valued metric space, meanwhile the G-metric space and the C *-algebra valued metric space itself is a generalization of known metric space. The G-metric generalized the domain of metric from X × X into X × X × X, the C *-algebra valued metric generalized the codomain from real number into C *-algebra, and the C *-algebra valued G-metric space generalized both the domain and the codomain. In C *-algebra valued G-metric space, there is one theorem that is similar to the Banach-Caccioppoli Fixed Point Theorem, called by fixed point theorem with contractive mapping on C *-algebra valued G-metric space. This theorem is already proven by Congcong Shen, Lining Jiang, Zhenhua Ma (2018). In this paper, we discuss another new proof of this theorem by using the metric function d(x, y) = max{G(x, x, y),G(y, x, x)}.

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 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.

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