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2011, vol. 15, br. 1, str. 31-39
Common fixed points for nonexpansive type mappings
(naslov ne postoji na srpskom)
J.K. Puram Choti Mukhani, Haldwani - Nainital, Uttarakhand, India

e-adresavyomeshpant@yahoo.co.in
Ključne reči: nonexpansive conditions; nocompatible mappings; pointwise R-weak commutativity; R-weak commutativity; contractive conditions; property (E.A); conditionally commuting maps
Sažetak
(ne postoji na srpskom)
The aim of the present paper is to obtain common fixed point theorems for three mappings satisfying nonexpansive type condition. For this purpose we use the notion of pointwise R-weak commutativity or R-weak commutativity of type (Ag) but without assuming the completeness of the space or continuity of the mappings involved. We further generalize the results obtained in first three theorems by replacing the condition of noncompatibility of maps with the property (E.A). 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 are, thus, able to provide one more answer to the problem posed by Rhoades [13] regarding the existence of contractive definition which is strong enough to generate fixed point but does not forces the maps to become continuous. In Theorem 6, we use the notion of conditionally commuting maps recently introduced by Pant and Pant [12] and prove a common fixed point theorem under minimal commutative condition.
Reference
Aamri, M., el Moutawakil, D. (2002) Some new common fixed point theorems under strict contractive conditions. Journal of Mathematical Analysis and Applications, 270(1), pp. 181-188
Jungck, G. (1986) Compatible mappings and common fixed points. Internat. J Math. Math. Sci., 9, 4, 771-779
Jungck, G., Rhoades, B.E. (2006) Fixed point theorems for occasionally weakly compatible mappings. Fixed Point Theory, 7 (2), 287-296
Pant, R.P. (1999) R-weak commutativity and common fixed points. Soochow J. Math., 25, pp. 37-42
Pant, R.P., Pant, V. (2000) Lipschitz type condition and common fixed points. J. Indian Math. Soc. (N.S.), 67(4): 179
Pant, R.P. (1994) Common fixed point of non-commuting mappings. J Math. Anal. Appl, 188, 436-440
Pant, R.P. (1998) R-weak commutativity and common fixed points of noncompatible maps. Ganita, 49, pp. 19-27
Pant, R.P. (1998) Common fixed point theorems for noncontractive maps. J Math. Anal. Appl, 226, 251-258
Pant, R.P. (1999) Common fixed points of Lipschitz type mapping pairs. J Math. Anal. Appl, 240, 280-283
Pant, R.P. (1999) Discontinuity and fixed points. J Math. Anal. Appl, 240, 284-289
Pant, V., Pant, R.P. (2010) Common fixed points of conditionally commuting maps. Fixed Point Theory, 11 (1), 113-118
Pathak, H.K., Cho, Y.J., Kang, S.M. (1997) Remarks on R-weakly commuting mappings and common fixed point theorems. Bull. Korean Math. Soc, 34, 247-257
Rhoades, B.E. (1988) Contractive definitions and continuity. Contemporary Math, 72, 233-245
 

O članku

jezik rada: engleski
vrsta rada: neklasifikovan
DOI: 10.5937/MatMor1101031P
objavljen u SCIndeksu: 27.03.2012.