East Asian mathematical journal
- Volume 22 Issue 1
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- Pages.35-51
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- 2006
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- 1226-6973(pISSN)
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- 2287-2833(eISSN)
COMMON FIXED POINTS OF A LIMIT WEAK COMPATIBLE PAIR OF A MULTIVALUED MAPPING AND A SINGLE VALUED MAPPING IN D-METRIC SPACES
- Singh, Bijendra (S. S. in Mathematics, Vikram University) ;
- Jain, Shobha (Shri Vaishnav Institute of Management) ;
- jain, Shishir (Shri Vaishnav Institute of Technology and Science)
- Published : 2006.06.30
Abstract
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.
Keywords
- D-metric space;
- limit weak compatible maps;
- weak compatible maps;
- set-valued map;
- orbit;
- bounded orbit;
- unique common fixed point