scholarly journals Some common fixed point theorems for converse commuting mappings via implicit relation

2013 ◽  
Vol 17 (2) ◽  
pp. 79-87
Author(s):  
Xiao-Lan Liu ◽  
Sunny Chauhan ◽  
Shikha Chaudhari
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Implicit Relation ◽  
Common Fixed Point Theorems ◽  
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  

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 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.

scholarly journals Unified common fixed point theorems in complex valued metric spaces via an implicit relation with applications

2019 ◽  
Vol 38 (4) ◽  
pp. 9-29
Author(s):  
Waleed Mohd Alfaqih ◽  
Mohammad Imdad ◽  
Fayyaz Rouzkard
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Implicit Relation ◽  
Common Solution ◽  
Weakly Compatible ◽  
Urysohn Integral Equations ◽  
Complex Valued ◽  
Common Fixed Point Theorems

The purpose of this paper is to prove some common fixed point theorems for two pairs of weakly compatible mappings in complex valued metric spaces satisfying an implicit relation. Several illustrative examples are given which demonstrate the usefulness of our utilized implicit relation. Beside generalizing and improving several well known core results of the existing literature we can deduce several new contractions which have not obtained before in complex valued metric spaces. As an application of our results, we prove the existence and uniqueness of common solution of Hammerstein as well as Urysohn integral equations.

Common fixed point theorems for hybrid pair of mappings

Filomat ◽  
2017 ◽  
Vol 31 (10) ◽  
pp. 2975-2979
Author(s):  
P.C. Mathpal ◽  
L.K. Joshi ◽  
Mahesh Joshi ◽  
N. Chandra
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Type Condition ◽  
Hybrid Pair ◽  
Common Fixed Point Theorems ◽  
Commuting Mappings

In this paper we define the concept of conditionally commuting mappings and establish some common fixed point theorems for hybrid pair of mappings satisfying a nonexpansive type condition.

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