Coincidence points an best proximity pair results for R-subweakly commuting multimaps

• Autorzy: O'Regan D. , Shahzad N.
• Języki publikacji: EN

Abstrakty

EN

Some coincidence point theorems for R-subweakly commuting mappings satisfying a general contractive condition are proved. As applications, some best proximity pair results are also obtained and several related results in the literature are extended to a new class of noncommuting mappings.

Słowa kluczowe

EN

coincidence point theorem; mappings; nonexpansive map; best proximity pair; metric space

PL

teoria wspólnych punktów; odwzorowania; odwzorowanie nieekspansywne; twierdzenie o bliskości par; przestrzeń metryczna

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2006
• Tom: Vol. 39, nr 4
• Strony: 845--854
• Opis fizyczny: Bibliogr. 23 poz.

Twórcy

autor

O'Regan D.

autor

Shahzad N.

• Department of Mathematics National University of Ireland Galway, Ireland

Bibliografia

• [1] H. F. Bohnenblust and S. Karlin, On a theorem of Ville Contributions to the theory of games, (Edited by Kuhn and Tucker, University Press, Princeton), I (1950), 155–160.
• [2] Y. J. Cho, B. Fisher and G. S. Jeong, Coincidence theorems for nonlinear hybrid contractions, Internat. J. Math. Math. Sci. 20 (1997), 249–256.
• [3] W. G. Dotson, Jr., Fixed point theorems for nonexpansive mappings on starshaped subsets of Banach spaces, J. London Math. Soc. 4 (1972), 408–410.
• [4] Ky Fan, Extensions of two fixed point theorems of F. E. Browder, Math. Z. 112 (1969), 234–240.
• [5] S. Itoh and W. Takahashi, Single-valued mappings, multivalued mappings and fixed point theorems, J. Math. Anal. Appl. 59 (1977), 514–521.
• [6] G. Jungck and S. Sessa, Fixed point theorems in best approximation theory, Math. Japonica 42 (1995), 249–252.
• [7] S. Kakutani, A generalization of Brouwer fixed point theorem Duke Math. J. 8 (1941), 457–459.
• [8] H. Kaneko, Single-valued and multivalued f-contractions, Boll. Un. Mat. Ital. 6 (1985), 29–33.
• [9] W. A. Kirk, S. Reichand P. Veeramani, Proximinal retracts and best proximity pair theorems Numer. Funct. Anal. Optim. 24 (2003), 851–862.
• [10] E. Lami Dozo, Multivalued nonexpansive mappings and Opial's condition, Proc. Amer. Math. Soc. 38 (1973), 286–292.
• [11] A. Latifand I. Tweddle, On multivalued f-nonexpansive maps, Demonstratio Math. 32 (1999), 565–574.
• [12] N. Mizoguchi and W. Takahashi, Fixed point theorem for multivalued mappings on complete metric spaces, J. Math. Anal. Appl. 141 (1989), 177–188.
• [13] S. B. Nadler, Jr., Multivalued contraction mappings, Pacific J. Math. 30 (1969), 475–488.
• [14] Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967), 591–597.
• [15] D. O'Regan, N. Shahzad and R. Agarwal, Birkhoff-Kellogg and best proximity pair results, Bull. Belgian Math. Soc. (Simon Stevin) (in press).
• [16] D. O'Regan, N. Shahzad and R. Agarwal, Common fixed point theory for compatible maps Nonlinear Anal. Forum 8 (2003), 179–222.
• [17] R. A. Rashwan, A coincidence theorem for contractive type multivalued mappings, J. Egyptian Math. Soc. 5 (1997), 47–55.
• [18] B. E. Rhoades, On multivalued f-nonexpansive maps, Fixed Point Theory and Appl. 2 (2001), 89–92.
• [19] S. Sadiq Basha and P. Veeramani, Best approximations and best proximity pairs, Acta Sci. Math. (Szeged) 63 (1997), 289–300.
• [20] S. Sadiq Basha and P. Veeramani, Best proximity pair theorems for multifunctions with open fibres, J. Approx. Theory 103 (2000), 119–129.
• [21] N. Shahzad, Coincidence points and and R-subweakly commuting multivalued maps, Demontratio Math. 36 (2003), 427–431.
• [22] N. Shahzad and T. Kamran, Coincidence points and R-weakly commuting maps Arch. Math. (Brno) 37 (2001), 179–183.
• [23] P. S. Srinivasan, Best proximity pair theorems, Acta Sci. Math. (Szeged) 67 (2001), 421–429.