scholarly journals Erratum to: “Skew-commuting and commuting mappings in rings” [Aequationes Math. 64 (2002), 136–144]

2005 ◽  
Vol 70 (1-2) ◽  
pp. 199-200
Author(s):  
Kyoo-Hong Park ◽  
Yong-Soo Jung
Keyword(s):  
Aequationes Math ◽  
Commuting Mappings

scholarly journals Fixed points of quasi-nonexpansive mappings

1972 ◽  
Vol 13 (2) ◽  
pp. 167-170 ◽  
Author(s):  
W. G. Dotson
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Linear Space ◽  
Complex Plane ◽  
Normed Linear Space ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
The Other ◽  
Commuting Mappings ◽  
Analytic Mappings

A self-mapping T of a subset C of a normed linear space is said to be non-expansive provided ║Tx — Ty║ ≦ ║x – y║ holds for all x, y ∈ C. There has been a number of recent results on common fixed points of commutative families of nonexpansive mappings in Banach spaces, for example see DeMarr [6], Browder [3], and Belluce and Kirk [1], [2]. There have also been several recent results concerning common fixed points of two commuting mappings, one of which satisfies some condition like nonexpansiveness while the other is only continuous, for example see DeMarr [5], Jungck [8], Singh [11], [12], and Cano [4]. These results, with the exception of Cano's, have been confined to mappings from the reals to the reals. Some recent results on common fixed points of commuting analytic mappings in the complex plane have also been obtained, for example see Singh [13] and Shields [10].

Skew-commuting and Commuting Mappings in Rings with Left Identity

2004 ◽  
Vol 46 (1-2) ◽  
pp. 123-129 ◽  
Author(s):  
R. K. Sharma ◽  
Basudeb Dhara
Keyword(s):  
Left Identity ◽  
Commuting Mappings

scholarly journals Common fixed point theorems for occasionally converse commuting mappings in symmetric spaces

1970 ◽  
Vol 7 (1) ◽  
pp. 56-62
Author(s):  
HK Pathak ◽  
RK Verma
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Symmetric Spaces ◽  
The Other ◽  
Implicit Relation ◽  
Subject Classifications ◽  
Keywords And Phrases ◽  
Mathematics Subject Classifications ◽  
Common Fixed Point Theorems ◽  
Commuting Mappings

In this paper, we introduce the notion of occasionally converse commuting (occ) mappings. Every converse commuting mappings ([1]) are (occ) but the converse need not be true (see, Ex.1.1-1.3). By using this concept, we prove two common fixed point results for a quadruple of self-mappings which satisfy an implicit relation. In first result one pair is (owc) [5] and the other is (occ), while in second result both the pairs are (occ). We illustrate our theorems by suitable examples. Since, there may exist mappings which are (occ) but not conversely commuting, the Theorems 1.1[2], 1.2[2] and 1.3[3] fails to handle those mapping pairs which are only (occ) but not conversely commuting (like Ex.1.4). On the other hand, since every conversely commuting mappings are (occ), so our Theorem 3.1 and 3.2 generalizes these theorems and the main results of Pathak and Verma [6]-[7]   Mathematics Subject Classifications: 47H10; 54H25. Keywords and Phrases: commuting mappings; conversely commuting mappings; occasionally converse commuting (occ) mappings; set of commuting mappings; fixed point. DOI: http://dx.doi.org/ 10.3126/kuset.v7i1.5422 KUSET 2011; 7(1): 56-62  

Commuting Mappings and Fixed Points

1976 ◽  
Vol 83 (4) ◽  
pp. 261-263 ◽  
Author(s):  
Gerald Jungck
Keyword(s):  
Fixed Points ◽  
Commuting Mappings

scholarly journals A New Common Fixed Point Theorem for Three Commuting Mappings

Axioms ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 105
Author(s):  
Meryeme El Harrak ◽  
Ahmed Hajji
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Contractive Condition ◽  
Darbo’S Fixed Point Theorem ◽  
Common Fixed Point Theorem ◽  
Commuting Mappings

In the present paper, we propose a common fixed point theorem for three commuting mappings via a new contractive condition which generalizes fixed point theorems of Darbo, Hajji and Aghajani et al. An application is also given to illustrate our main result. Moreover, several consequences are derived, which are generalizations of Darbo’s fixed point theorem and a Hajji’s result.

scholarly journals Common Fixed Point Theorems for Conversely Commuting Mappings Using Implicit Relations

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Sunny Chauhan ◽  
Huma Sahper
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Menger Spaces ◽  
Common Fixed Point Theorems ◽  
Commuting Mappings

The object of this paper is to utilize the notion of conversely commuting mappings due to Lü (2002) and prove some common fixed point theorems in Menger spaces via implicit relations. We give some examples which demonstrate the validity of the hypotheses and degree of generality of our main results.

scholarly journals Some Generalizations of Jungck's Fixed Point Theorem

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
J. R. Morales ◽  
E. M. Rojas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Distance Functions ◽  
Integral Type ◽  
Compatible Pair ◽  
Altering Distance ◽  
Commuting Mappings

We are going to generalize the Jungck's fixed point theorem for commuting mappings by mean of the concepts of altering distance functions and compatible pair of mappings, as well as, by using contractive inequalities of integral type and contractive inequalities depending on another function.

scholarly journals Common periodic points for a class of continuous commuting mappings on an interval

2003 ◽  
Vol 2003 (16) ◽  
pp. 1043-1046
Author(s):  
Shin Min Kang ◽  
Weili Wang
Keyword(s):  
Periodic Points ◽  
Commuting Mappings

The existence of common periodic points for a family of continuous commuting self-mappings on an interval is proved and two illustrative examples are given in support of our theorem and definition.

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