Common fixed point theorems for set-valued and single-valued mappings

• Autorzy: Ahmed, M. A.
• Języki publikacji: EN

Abstrakty

EN

The concepts of δ-compatibility and weakly compatibility between a set-valued mapping and a single-valued mapping of Jungck and Rhoades [8, 9] are used to prove some common fixed point theorems on metric spaces. Generalizations of known results are thereby obtained. In particular, theorems by Fisher [2] and Khan, Kubiaczyk and Sessa [11] are generalized. An example is given to support our generalization.

Słowa kluczowe

PL

twierdzenie o punkcie stałym; odwzorowanie

EN

fixed point theorem; mappings

• Czasopismo: Demonstratio Mathematica
• Rocznik: 2003
• Tom: Vol. 36, nr 2
• Strony: 471--481
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Ahmed, M. A.

• Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516, Egypt,
• Department of Mathematics, Teachers College, P.O. Box 4341, Riyadh 11491, Kindom of Saudi Arabia

Bibliografia

• [1] T.-H. Chang, Fixed point theorems of contractive type set-valued mappings, Math. Japonica 38, No. 4 (1993), 675-690.
• [2] B. Fisher, Common fixed points of mapppings and set-valued mappings on a metric spaces, Kyungpook Math. J. 25 (1985), 35-42.
• [3] B. Fisher and S. Sessa, Common fixed points of two pairs of weakly commuting mapppings, Univ. u Novom Sadu, Zb. Rad. Period.-Mat. Fak. Ser. Mat. 18(1986), 45-59.
• [4] B. Fisher and S. Sessa, Two common fixed point theorems for weakly commuting mapppings, Periodica Math. Hungarica 20, No. 3(1989), 207-218.
• [5] G. S. Jeong and B. E. Rhoades, Some remarks for involving fixed point theorems for more than two maps, Indian J. Pure Appl. Math. 28, No. 9 (1997), 1171-1196.
• [6] G. Jungck, Compatible mapppings and common fixed points, Internat. J. Math. Math. Sci. 9 (1986), 771-779.
• [7] G. Jungck, Common fixed points of commuting and compatible maps on compacta, Proc. Amer. Math. Soc. 103 (1988), 977-983.
• [8] G. Jungck and B. E. Rhoades, Some fixed point theorems for compatible maps, Internat. J. Math. Math. Sci. 16, No. 3(1993), 417-428.
• [9] G. Jungck and B. E. Rhoades, Fixed points for set valued functions without continuity, Indian J. Pure Appl. Math.16, No. 3(1998), 227-238.
• [10] S. M. Kang and B. E. Rhoades, Fixed points for four mappings, Math. Japonica 37 (1992), 1053-1059.
• [11] M. S. Khan, I. Kubiaczyk and S. Sessa, On set-valued and single-valued mappings with common fixed points, Bull. Malaysia Math. Soc. 2, No. 10(1987), 71-81.
• [12] S. Kyzyska and I. Kubiaczyk, Fixed point theorems for upper semicontinuous and weakly-weakly upper semicontinuous multivalued mappings, Math. Japonica 47, No. 2 (1998), 237-240.
• [13] R. A. Rashwan, A common fixed point theorem in uniformly convex Banach spaces, Italian J. Pure Appl. Math. N. 3(1998), 117-126.
• [14] R. A. Rashwan and M. A. Ahmed, Common fixed points for δ-compatible mappings, Southwest J. Pure Appl. Math. 1(1996), 51-61.
• [15] R. A. Rashwan and M. A. Ahmed, Common fixed points for weakly compatible mappings, Italian J. Pure Appl. Math. N. 8(2000), 33-44.
• [16] B. E. Rhoades, Common fixed points of compatible set-valued mappings, Publ. Math.Debrecen 48, No. 3-4 (1996), 237-240.
• [17] S. Sessa, On a weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math. (Beograd)32, No. 46(1982), 149-153.
• [18] S. Sessa and M. S. Khan, Some remarks in best approximation theory, Math. J. Toyoma Univ. 17(1994), 151-165.