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SEMI-COMPATIBILITY AND FIXED POINT THEOREM IN MENGER SPACE
Bijendra Singh,Shishir Jain 충청수학회 2004 충청수학회지 Vol.17 No.1
In this paper, the concept of semi-compatibility in Menger space is introduced and it is used to prove results on the existence of a unique common fixed point of four self-maps. These results are a very wide improvement of Mishra [8], Dedeic and Sarapa [3, 4], Cain and Kasril [1], and Sehgal and Bharucha Reid [10].
Singh, Bijendra,Jain, Shobha 충청수학회 2005 충청수학회지 Vol.18 No.1
The object of this paper is to prove two unique common fixed point theorems for a pair of a set-valued map and a self map satisfying a general contractive condition using orbital concept and weak-compatibility of the pair. One of these results generalizes substantially, the result of Dhage, Jennifer and Kang [4]. Simultaneously, its implications for two maps and one map improves and generalizes the results of Dhage [3], and Rhoades [11]. All the results of this paper are new.
COMMON FIXED POINTS OF WEAK-COMPATIBLE MAPS ON D-METRIC SPACE
Singh, Bijendra,Jain, Shobha 충청수학회 2004 충청수학회지 Vol.17 No.2
In [4], Dhage proved a result for common fixed point of two self-maps satisfying a contractive condition in D-metric spaces. This note proves a fixed point theorem for five self-maps under weak-compatibility in D-metric space which improves and generalizes the above mentioned result.
Singh, Bijendra,Jain, Shishir,Jain, Shobha The Youngnam Mathematical Society Korea 2007 East Asian mathematical journal Vol.23 No.2
The object of this paper is to introduce the notion of semi-compatible maps in fuzzy metric spaces, fuzzy 2-metric spaces and fuzzy 3-metric spaces and to establish three common fixed point theorems for these spaces for four self-maps. These results improve, extend and generalize the results of [16]. As an application, these results have been used to obtain translation and generalization of Grabeic's contraction principle in the new settings. All the result presented in this paper are new.
SEMI-COMPATIBILITY, COMPATIBILITY AND FIXED POINT THEOREMS IN FUZZY METRIC SPACE
Singh, Bijendra,Jain, Shishir 충청수학회 2005 충청수학회지 Vol.18 No.1
The object of this paper is to introduce the concept of a pair of semi-compatible self-maps in a fuzzy metric space to establish a fixed point theorem for four self-maps. It offers an extension of Vasuki [10] to four self-maps under the assumption of semi-compatibility and compatibility, repsectively. At the same time, these results give the alternate results of Grebiec [5] and Vasuki [9] as well.
SEMI-COMPATIBILITY AND FIXED POINT THEOREM IN MENGER SPACE USING IMPLICIT RELATION
Singh, Bijendra,Jain, Shishir The Youngnam Mathematical Society Korea 2005 East Asian mathematical journal Vol.21 No.1
In this paper the concept of semi-compatibility has been introduced in Menger space and it has been applied to prove results on existence of unique common fixed point of four self maps satisfying an implicit relation. It results in a generalization of Banach contraction principle established by Sehgal and Bharucha-Reid in [8] All the result presented in this paper are new.
SEMI-COMPATIBILITY AND FIXED POINTS OF EXPANSION MAPPINGS IN 2-METRIC SPACES
Singh, Bijendra,Jain, Shobha 충청수학회 2004 충청수학회지 Vol.17 No.2
This paper introduces the notion of semi-compatible self-maps in 2-metric spaces and establishes a fixed point theorem for four self-maps, satisfying an implicit relation through semi-compatibility of a pair of self-maps. This results in another fixed point theorem for four expansion maps which generalizes and improves many results of Kang et. al. [5] with an application.
SEMI-COMPATIBILITY AND FIXED POINTS OF EXPANSION MAPPINGS IN 2-METRIC SPACES
Bijendra Singh,Shobha Jain 충청수학회 2004 충청수학회지 Vol.17 No.2
This paper introduces the notion of semi-compatible self-maps in 2-metric spaces and establishes a fixed point theorem for four self-maps, satisfying an implicit relation through semi-compatibility of a pair of self-maps. This results in another fixed point theorem for four expansion maps which generalizes and improves many results of Kang et. al. [5] with an application.
COMMON FIXED POINTS OF WEAK–COMPATIBLE MAPS ON D–METRIC SPACE
Bijendra Singh,Shobha Jain 충청수학회 2004 충청수학회지 Vol.17 No.2
In [4], Dhage proved a result for common fixed point of two self-maps satisfying a contractive condition in D-metric spaces. This note proves a fixed point theorem for five self-maps under weakcompatibility in D-metric space which improves and generalizes the above mentioned result.
SEM-COMPATIBILITY AND FIXED POINT THEOREM IN MENGER SPACE
Singh, Bijendra,Jain, Shishir 충청수학회 2004 충청수학회지 Vol.17 No.1
In this paper, the concept of semi-compatibility in Menger space is introduced and it is used to prove results on the existence of a unique common fixed point of four self-maps. These results are a very wide improvement of Mishra [8], Dedeic and Sarapa [3, 4], Cain and Kasril [1], and Sehgal and Bharucha Reid [10].