scholarly journals Generalization of common fixed point theorems for weakly commuting maps by altering distances

2000 ◽  
Vol 31 (3) ◽  
pp. 243-250 ◽  
Author(s):  
K. P. R. Sastry ◽  
S. V. R. Naidu ◽  
G. V. R. Babu ◽  
G. A. Naidu
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Complete Metric Space ◽  
Commuting Maps ◽  
Common Fixed Point Theorems ◽  
Unique Common Fixed Point

The main purpose of this paper is to obtain conditions for the existence of a unique common fixed point for four selfmaps on a complete metric space by altering distances between the points.

scholarly journals Common fixed point theorems for semigroups on metric spaces

1999 ◽  
Vol 22 (2) ◽  
pp. 377-386 ◽  
Author(s):  
Young-Ye Huang ◽  
Chung-Chien Hong
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Common Fixed Point Theorems ◽  
Lipschitzian Semigroup ◽  
Common Fixed Point Theorem ◽  
Unique Common Fixed Point

This paper consists of two main results. The first one shows that ifSis a left reversible semigroup of selfmaps on a complete metric space(M,d)such that there is a gauge functionφfor whichd(f(x),f(y))≤φ(δ(Of (x,y)))forf∈Sandx,yinM, whereδ(Of (x,y))denotes the diameter of the orbit ofx,yunderf, thenShas a unique common fixed pointξinMand, moreover, for anyfinSandxinM, the sequence of iterates{fn(x)}converges toξ. The second result is a common fixed point theorem for a left reversible uniformly Lipschitzian semigroup of selfmaps on a bounded hyperconvex metric space(M,d).

COMMON FIXED POINT THEOREM FOR TWO MAPPINGS IN bi-b-METRIC SPACE

2022 ◽  
Vol 11 (1) ◽  
pp. 25-34
Author(s):  
V.D. Borgaonkar ◽  
K.L. Bondar ◽  
S.M. Jogdand
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
The Common ◽  
Common Fixed Point Theorems ◽  
Common Fixed Point Theorem ◽  
Unique Common Fixed Point

In this paper we have used the concept of bi-metric space and intoduced the concept of bi-b-metric space. our objective is to obtain the common fixed point theorems for two mappings on two different b-metric spaces induced on same set X. In this paper we prove that on the set X two b-metrics are defined to form two different b-metric spaces and the two mappings defined on X have unique common fixed point.

scholarly journals Fixed Point Results on Multiplicative Semi-Metric Space

2020 ◽  
Vol 12 (3) ◽  
pp. 341-348
Author(s):  
B. Vijayabaskerreddy ◽  
V. Srinivas
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Compatible Mappings ◽  
Weakly Compatible ◽  
Continuous Mappings ◽  
Common Fixed Point Theorems ◽  
Multiplicative Metric Space ◽  
Unique Common Fixed Point

  In this paper we introduce the notion of the Multiplicative Semi-Metric Space and proved common fixed point theorems. We establish fixed point theorems for four self-maps which can be extended to derive common fixed point theorems involving any finite number of mappings in Multiplicative Semi Metric Space. Further examples are discussed to show that compatible mappings of type-E, weakly compatible mappings and reciprocally-continuous mappings are weaker forms of compatible mappings and continuous mappings respectively. The main objective of this article is to prove the unique common fixed point theorems and employing the notion of the compatible mappings of type-E, reciprocally-continuous mappings in the Multiplicative Semi Metric Space. Our result generalizes the concept of Multiplicative Metric Space as it does not involve the multiplicative triangle inequality.

On common fixed points for a family of mappings

1975 ◽  
Vol 13 (2) ◽  
pp. 261-267 ◽  
Author(s):  
S.A. Husain ◽  
V.M. Sehgal
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Complete Metric Space ◽  
Common Fixed Points ◽  
Common Fixed Point Theorems

The purpose of this paper is to obtain some common fixed point theorems for a family of mappings in a complete metric space. The results herein improve some of the recent theorems of Kiyoshi Iséki (Bull. Austral. Math. Soc. 10 (1974), 365–370).

scholarly journals Common fixed point theorems for two mappings satisfying some conditions

2000 ◽  
Vol 62 (1) ◽  
pp. 75-85
Author(s):  
Jeong Sheok Ume ◽  
Jong Kyu Kim
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Complete Metric Space ◽  
Common Fixed Point Theorems

In this paper, using the concept of w-distance, we first prove common fixed point theorems in a complete metric space. Then these theorems are used to improve Kannan's fixed point theorem, Ćirić's fixed point theorem, Kada, Suzuki and Takahashi's fixed point theorem and Ume's fixed point theorem.

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