Common Fixed Point Theorems For Finite Number Of Mappings Without Continuity And Compatibility In Menger Spaces
Journal: International Journal of Scientific & Technology Research (Vol.2, No. 2)Publication Date: 2013-02-25
Abstract
Theorem 1 Let A B S T I J L U P and Q be self maps on a Menger space X F t with ta a a for all a 0 1 satisfying1.1PX ABILX QX STJUX1.2P STJU or Q ABIL satisfies the property S-B1.3 there exists k 0 1 such that FPxQyku min FABILySTJUxuFPxSTJUxu FQyABILyu FQySTJUxu FPxABILyufor all x y X and u 01.4 if one of PX ABILX STJUX or QX is a closed subspace of X then i P and STJU have a coincidence point and ii Q and ABIL have a coincidence point.Further if 1.5 AB BA AI IA AL LA BI IB BL LB IL LI QL LQ QI IQ QB BQ ST TS SJ JS SU US TJ JTTU UT JU UJ PU UP PJ JP PT TP1.6 the pairs P STJU and Q ABIL are weakly compatible.Then A B S T I J L U P and Q have a unique common point in X.
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Last modified: 2013-04-13 21:56:02