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  

scholarly journals Common fixed point theorems under contractive conditions of integral type in symmetric spaces

2013 ◽  
Vol 46 (4) ◽  
Author(s):  
F. Merghadi ◽  
C. Godet-Thobie
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Symmetric Spaces ◽  
Fixed Point Theorems ◽  
Integral Type ◽  
Weak Compatibility ◽  
Common Fixed Point Theorems

AbstractThe purpose of this paper is to prove common fixed point theorems for a family of mappings in symmetric spaces using the property (E.A) and weak compatibility or occasionally weak compatibility. Our results extend some recent results.

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 Common Fixed Point Theorems of Greguš Type (ϕ,ψ)-Weak Contraction for R-Weakly Commuting Mappings in 2-Metric Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Penumarthy Parvateesam Murthy ◽  
Uma Devi Patel
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Spaces ◽  
Weak Contraction ◽  
Weakly Commuting Mappings ◽  
Set Valued Mappings ◽  
Commuting Maps ◽  
Common Fixed Point Theorems ◽  
Common Fixed Point Theorem ◽  
Commuting Mappings

The main purpose of this paper is to establish a common fixed point theorem for set valued mappings in 2-metric spaces by generalizing a theorem of Abd EL-Monsef et al. (2009) and Murthy and Tas (2009) by using (ϕ,ψ)-weak contraction in view of Greguš type condition for set valued mappings using R-weakly commuting maps.

scholarly journals On compatible mappings satisfying an implicit relation in common fixed point consideration

2002 ◽  
Vol 33 (3) ◽  
pp. 245-252 ◽  
Author(s):  
Sushil Sharma ◽  
Bhavana Deshpande
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Compatible Mappings ◽  
Implicit Relation ◽  
Common Fixed Point Theorems

In this paper, we prove some common fixed point theorems for compatible mappings satisfying an implicit relation.

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