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Bull. Korean Math. Soc. 1997; 34(2): 247-257

Printed June 1, 1997

Copyright © The Korean Mathematical Society.

Remarks on $R$-weakly commuting mappings and common fixed point theorems

H. K. Pathak, Y. J. Cho, and S. M. Kang

, Gyeongsang National University, Gyeongsang National University

Abstract

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In this paper, we observe that the results of Pant do not hold if we drop either completeness of the space $X$ or continuity of the maps $f$ and $g$ over the whole space $X$ by giving two examples and improve them by using the new concepts of R-weakly commuting mappings of type $(A_f)$ and $(A_g)$.

Keywords: R-weakly commuting mappings, R-weakly commuting mappings of types $(A_f)$ and $(A_g)$, common fixed point

MSC numbers: Primary 54H25, Secondary 47H10

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