Fixed point and homotopy result for mappings satisfying an implicit relation

2007 ◽  
Vol 27 (2) ◽  
pp. 349 ◽  
Author(s):  
I. Altun ◽  
D. Turkoglu
Keyword(s):  
Fixed Point ◽  
Implicit Relation ◽  
Homotopy Result

scholarly journals Fixed Point Problems in Cone Rectangular Metric Spaces with Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Muhammad Nazam ◽  
Anam Arif ◽  
Hasan Mahmood ◽  
Sang Og Kim
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Problems ◽  
Implicit Relation ◽  
Rectangular Metric Space ◽  
Homotopy Result

In this paper, we introduce an ordered implicit relation and investigate some new fixed point theorems in a cone rectangular metric space subject to this relation. Some examples are presented as illustrations. We obtain a homotopy result as an application. Our results generalize and extend several fixed point results in literature.

scholarly journals Some results in cone metric spaces with applications in homotopy theory

2020 ◽  
Vol 18 (1) ◽  
pp. 295-306 ◽  
Author(s):  
Muhammad Nazam ◽  
Anam Arif ◽  
Hasan Mahmood ◽  
Choonkil Park
Keyword(s):  
Fixed Point ◽  
Homotopy Theory ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
The Self ◽  
Cone Metric Spaces ◽  
Implicit Relation ◽  
Contractive Mappings ◽  
Homotopy Result ◽  
Cone Metric

Abstract The self-mappings satisfying implicit relations were introduced in a previous study [Popa, Fixed point theorems for implicit contractive mappings, Stud. Cerc. St. Ser. Mat. Univ. Bacău 7 (1997), 129–133]. In this study, we introduce self-operators satisfying an ordered implicit relation and hence obtain their fixed points in the cone metric space under some additional conditions. We obtain a homotopy result as an application.

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 The N-Fuzzy Metric Spaces and Mappings with Application

2015 ◽  
Vol 55 (1) ◽  
pp. 133-151 ◽  
Author(s):  
Neeraj Malviya
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Implicit Relation ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric

Abstract In the present paper, we introduce the notion of N-fuzzy metric spaces (NFMSs), Pseudo N-fuzzy metric spaces and describe some of their properties. Also we prove a fixed point theorem using implicit relation in N-fuzzy metric spaces.

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