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초록· 키워드
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The aim of the present paper is three fold. Firstly, we obtain
common fixed point theorems for a pair of selfmaps satisfying nonexpansive
or Lipschitz type condition by using the notion of pointwise R-weak
commutativity but without assuming the completeness of the space or
continuity of the mappings involved (Theorem 1, Theorem 2 and Theorem
3). Secondly, we generalize the results obtained in first three theorems
for four mappings by replacing the condition of noncompatibility
of maps with the property (E.A) and using the R-weak commutativity
of type (Ag) (Theorem 4). Thirdly, in Theorem 5, we show that if the
aspect of noncompatibility is taken in place of the property (E.A), the
maps become discontinuous at their common fixed point. We, thus, provide
one more answer to the problem posed by Rhoades [11] regarding
the existence of contractive definition which is strong enough to generate
fixed point but does not forces the maps to become continuous.
목차
등록된 정보가 없습니다.
참고문헌 (11)
참고문헌 신청
B. E. Rhoades / 1988 / Contractive definitions and continuity, Fixed point theory and its applications (Berkeley, CA, 1986) / Contemporary Mathematics 72 : 233 ~ 245
G. Jungck / 1986 / Compatible mappings and common fixed points, Internat / International Journal of Mathematics and Mathematical Sciences 9 (4) : 771 ~ 779
H. K. Pathak / 1997 / Remarks on R-weakly commuting mappings and common fixed point theorems / Bulletin of the Korean Mathematical Society 34 (2) : 247 ~ 257
M. Aamri / 2002 / Some new common fixed point theorems under strict contractive conditions / Journal of Mathematical Analysis and Applications 270 (1) : 181 ~ 188
R. P. Pant / 1994 / Common fixed points of noncommuting mappings / Journal of Mathematical Analysis and Applications 188 (2) : 436 ~ 440
G. Jungck / 1986 / Compatible mappings and common fixed points, Internat / International Journal of Mathematics and Mathematical Sciences 9 (4) : 771 ~ 779
H. K. Pathak / 1997 / Remarks on R-weakly commuting mappings and common fixed point theorems / Bulletin of the Korean Mathematical Society 34 (2) : 247 ~ 257
M. Aamri / 2002 / Some new common fixed point theorems under strict contractive conditions / Journal of Mathematical Analysis and Applications 270 (1) : 181 ~ 188
R. P. Pant / 1994 / Common fixed points of noncommuting mappings / Journal of Mathematical Analysis and Applications 188 (2) : 436 ~ 440
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