Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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RENARKS ON REWEAKLY COMMUTING MAPPONGS AND COMMON FIXED POINT THEOREMS

  • Pathak, H.-K (Y. J. Cho Department of Mathematics, Kalyan Mahavidyalaya, Bhilai Nagar (M.P.) 490006, India) ;
  • Cho, Y.-J (Department of Mathematics, Gyeongsang National University, Chinju 660-701) ;
  • Kang, S.-M (Department of Mathematics, Gyeongsang National University, Chinju 660-701)
  • Published : 1997.05.01
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Abstract

It was the turning point in the "fixed point arena" when the notion of weak commutativity was introduced by Sessa [9] as a sharper tool to obtain common fixed points of mappings. As a result, all the results on fixed point theorems for commuting mappings were easily transformed in the setting of the new notion of weak commutativity of mappings. It gives a new impetus to the studying of common fixed points of mappings satisfying some contractive type conditions and a number of interesting results have been found by various authors. A bulk of results were produced and it was the centre of vigorous research activity in "Fixed Point Theory and its Application in various other Branches of Mathematical Sciences" in last two decades. A major break through was done by Jungck [3] when he proclaimed the new notion what he called "compatibility" of mapping and its usefulness for obtaining common fixed points of mappings was shown by him. There-after a flood of common fixed point theorems was produced by various researchers by using the improved notion of compatibility of mappings. of compatibility of mappings.

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References

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