• East Asian mathematical journal
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• v.22 no.1
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• pp.35-51
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• 2006

This paper deals with a general contraction. Two fixed-point theorems for a limit weak-compatible pair of a multi-valued map and a self map on a D-metric space have been established. These results improve significantly, the main results of Dhage, Jennifer and Kang [5] by reducing its assumption and generalizing its contraction simultaneously. At the same time some results of Singh, Jain and Jain [12] are generalized from a self map to a pair of a set-valued and a self map. Theorems of Veerapandi and Rao [16] get generalized and improved by these results. All the results of this paper are new.

• Journal of the Chungcheong Mathematical Society
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• v.18 no.1
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• pp.51-64
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• 2005

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.

• Journal of the Chungcheong Mathematical Society
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• v.17 no.2
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• pp.125-136
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• 2004

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.

• The Pure and Applied Mathematics
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• v.17 no.3
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• pp.205-209
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• 2010

We introduce the concept of semi-compatible and weak-compatible in $\cal{M}$-fuzzy metric space, and prove some fixed point theorem for four self maps satisfying some conditions in $\cal{M}$-fuzzy metric space.