Common fixed points for weakly compatible maps satisfying implicit relations without continuity

• Autorzy: Akkouchi M.
• Języki publikacji: EN

Abstrakty

EN

The purpose of this paper is to prove a common fixed point theorem for a set of four mappings on a complete metric space, using weak compatibility and a general implicit relation without appeal to continuity. Our results improve and generalize all the results obtained by A. Djoudi in a paper published in 2003.

Słowa kluczowe

EN

weakly compatible mappings; common fixed points; implicit relations

PL

odwzorowanie zgodne; wspólny punkt stały

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2011
• Tom: Vol. 44, nr 1
• Strony: 151--158
• Opis fizyczny: Bibliogr. 21 poz.

Twórcy

autor

Akkouchi M.

• Université Cadi Ayyad, Faculté Des Sciences-Semlalia, Département de Mathématiques, Av. Prince My Abdellah, Bp. 2390 Marrakech, Maroc

Bibliografia

• [1] A. Aliouche, A common fixed point theorem for weakly compatible mappings in compact metric spaces satisfying an implicit relation, Sarajevo J. Math. 3 (2007), 1–8.
• [2] A. Aliouche, A. Djoudi, Common fixed point theorems for mappings satisfying an implicit relation without decreasing assumption, Hacet. J. Math. Stat. 36 (2007), 11–18.
• [3] H. Bouhadjera, General common fixed point theorems for compatible mappings of type (C), Sarajevo J. Math. 1 (2005), 261–270.
• [4] A. Djoudi, A. Aliouche, A general common fixed point theorem for reciprocally continuous mappings satisfying an implicit relation, Austral. J. Math. Anal. Appl. 3 (2006), 1–7.
• [5] A. Djoudi, A common fixed point theorem for compatible mappings of type (B) in complete metric spaces, Demonstratio Math. 36 (2003), 463–470.
• [6] A. Djoudi, A unique common fixed point for compatible mappings of type (B) satisfying an implicit relation, Demonstratio Math. 36 (2003), 763–770.
• [7] M. Imdad, S. Kumar, M. S. Khan, Remarks on some fixed point theorems satisfying implicit relations, Radovi Mat. 1 (2002), 135–143.
• [8] G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci. 9 (1986), 771–779.
• [9] G. Jungck, P. P. Murthy, Y. J Cho, Compatible mappings of type (A) and common fixed points, Math. Japonica 38 (1993), 381–390.
• [10] G. Jungck, B. E. Rhoades, Fixed point for set valued functions without continuity, Indian J. Pure Appl. Math. 29 (3) (1998), 227–238.
• [11] G. Jungck, Common fixed points for non-continuous non-self maps on non metric spaces, Far East J. Math. Sci. 4 (1996), 199–215.
• [12] R. P. Pant, Common fixed points of noncommuting mappings, J. Math. Anal. Appl. 188 (1994), 436–440.
• [13] R. P. Pant, Common fixed points for four mappings, Bull. Calcutta. Math. Soc. 9 (1998), 281–286.
• [14] R. P. Pant, A common fixed point theorem under a new condition, Indian J. Pure. Appl. Math. 30 (1999), 147–152.
• [15] H. K. Pathak, M. S. Khan, Compatible mappings of type (B) and common fixed point theorems of Gregus type, Czechoslovak Math. J. 45 (1995), 685–698.
• [16] H. K. Pathak, Y. J. Cho, S. M. Kang, B. S. Lee, Fixed point theorems for compatible mappings of type (P) and applications to dynamic programming, Matematiche (Catania) 1 (1995), 15–33.
• [17] H. K. Pathak, Y. J. Cho, S. M. Khan, B. Madharia, Compatible mappings of type (C) and common fixed point theorems of Gregus type, Demonstratio Math. 31 (1998), 499–518.
• [18] V. Popa, Some fixed point theorems for compatible mappings satisfying an implicit relation, Demonstratio Math. 32 (1999), 157–163.
• [19] V. Popa, Common fixed point theorems for compatible mappings of type (A) satisfying an implicit relation, Stud. Cercet. “tiint. Ser. Mat. Univ. Bacău. 9 (1999), 165–172.
• [20] S. Sessa, B. Fisher, Common fixed points of weakly commuting mappings, Bull. Polish. Acad. Sci. Math. 36 (5-6) (1987), 149–153.
• [21] S. Sessa, On a weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math. (Beograd) (N.S.) 32 (1982), 149–153.[18] V. Popa, Some fixed point theorems for compatible mappings satisfying an implicit relation, Demonstratio Math. 32 (1999), 157–163.
• [19] V. Popa, Common fixed point theorems for compatible mappings of type (A) satisfying an implicit relation, Stud. Cercet. “tiint. Ser. Mat. Univ. Bacău. 9 (1999), 165–172.
• [20] S. Sessa, B. Fisher, Common fixed points of weakly commuting mappings, Bull. Polish. Acad. Sci. Math. 36 (5-6) (1987), 149–153.
• [21] S. Sessa, On a weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math. (Beograd) (N.S.) 32 (1982), 149–153.