Fixed points for set and single valued maps without continuity

• Autorzy: Djoudi A. , Khemis R.
• Języki publikacji: EN

Abstrakty

EN

In this paper we prove some common fixed point theorems for single valued and set valued mappings on a metric space. The theorems use minimal type commutativity and strict contractivity conditions with no continuity requirements. The theorems extend previous results on delta-compatible and continuous maps of [1] and [11] to a wider class of weakly compatible mappings not necessarly continuous. Also, a common fixed point theorem which applies to a sequence of set valued mappings is given.

Słowa kluczowe

EN

common fixed points; maps; weakly compatible maps; D-maps

PL

wspólny punkt stały; odwzorowania

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2005
• Tom: Vol. 38, nr 3
• Strony: 739--751
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Djoudi A.

• Institut de Mathematiques, Faculte des Sciences, Universite de Annaba, P.O. Box 12, 23000, Annaba, Algieria

autor

Khemis R.

• Institut de Mathematiques, Faculte des Sciences, Universite de Annaba, P.O. Box 12, 23000, Annaba, Algieria

Bibliografia

• [1] M. A. Ahmed, Common fixed point theorems for set-valued and single-valued mappings, Demonstratio Math. Vol 36. No.2 (2003), 471-481.
• [2] I. Beg & W. Shahzad, An application of a fixed point theorem to best simultaneous approximation, Approx. Theory Appl. & its Appl. 10 No. 3 (1994), 1-4.
• [3] M. J. Chen & S. Park, A unified approach to generalized quasi-varriational inequalities, Comm. Appl. Nonlinear Anal. 4 No.2 (1997), 103-118.
• [4] S. Czerwik, Multi-valued contractions in metric space, Aequationes Math. 16 (1977), 297-302.
• [5] S. Czerwik, Fixed point theorems and special solutions of functional equations, Scientific Papers of Silesian University, Katowice, 428 (1980) 1-83.
• [6] B. Fisher, Common fixed points of mappings and set-valued mappings, Rostock. Math. Kolloq. 18 (1981), 69-77.
• [7] B. Fisher & S. Sessa, Common fixed point theorems for weakly commuting mappings, Period. Math. Hungar. 20, No.3 (1989), 207-218.
• [8] G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci. 9 (1986), 771-779.
• [9] G. Jungck & B. E. Rhoades, Some fixed point theorems for compatible maps, Int. J. Math. Math. Sci. 16, No. 3 (1993), 417-428.
• [10] G. Jungck & B. E. Rhoades, Fixed points for set valued functions without continuity, Indian J. Pure Appl. Math. 16 No. 3 (1998), 227-238.
• [11] M. S. Khan, I. Kubiaczyk & S. Sessa, On set-valued and single-valued mappings with common fixed points, Bull. Malaysia Math. Soc. 2, No.10 (1987) , 71-81.
• [12] L. S. Liu, On common fixed points of single valued mappings, J. Qufu Norm. Univ. Nat. Sci. Ed. 18, No. 1 (1992), 6-10.
• [13] H. K. Pathak, S. N. Mishra & A. K. Kalinde, Some Gregus type common fixed point theorem with application, Demonstratio Math. Vol. 36 No. 2 (2003), 413-426.
• [14] S. Sessa, On weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math. (Beogard) 32, No. 46 (1982), 149-153.
• [15] S. Sessa, M. S. Khan & M. Imdad, Common fixed point theorem with weak commutativity condition, Glas. Mat. 21, No. 41 (1986), 225-235.
• [16] S. Sessa, M. S. Khan, Some remarks in best approximation theory, Math. J. Toyoma Univ. 17 (1994), 151-165.