Common fixed points of mappings not satisfying contractive condition

• Autorzy: Pant V. , Padaliya S. , Pant R. P.
• Języki publikacji: EN

Abstrakty

EN

The aim of this paper is to consider a new approach for obtaining common fixed point theorems in metric spaces by subjecting the triangle inequality to a Lipschitz type condition. For values of the Lipschitz constant k < 1/3 the condition reduces to a Banach type contractive condition and we get the results known so far. However, values of k ≥ 1/3 yield new result. It may be observed that in the setting of metric spaces k ≥ 1/3 generally does not ensure the existence of fixed points and there is no known method for dealing these cases. In Theorem 1 and Theorem 2 we provide results under a new condition. In the last section of this paper (Theorem 3 and Theorem 4) by using the (E.A) property introduced by Aamri and Moutawakil [2] we extend the results obtained in Theorem 1 and Theorem 2.

Słowa kluczowe

EN

noncompatible maps; common fixed point; contractive condition; E.A property

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2008
• Tom: Nr 40
• Strony: 71--77
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Pant V.

autor

Padaliya S.

autor

Pant R. P.

• A - 24, J.K. Puram, Choti Mukhani, Haldwani - 263 139, Nainital, Uttarakhand, India,

Bibliografia

• [1]JUNGCK G., Compatible Mappings and Common Fixed Points, Internat. J. Math. Sci., 9(1986), 771-779.
• [2]AAMRI M., MOUTAWAKIL D.EL, Some New Common Fixed Point Theorems Under Strict Contractive Conditions, J. Math. Anal. Appl., 270(2002), 181-188.
• [3]PANT R.P., Common Fixed Points of Noncommuting Mappings, J. Math. Anal. Appl, 188(1994), 436-440.
• [4]PANT R. P., Common Fixed Points of Contractive Maps, J. Math. Anal Appl,226(1998), 251-258.
• [5]PANT R.P., Discontinuity and Fixed Points, J. Math. Anal Appl, 240(1999), 284-289.
• [6]RHOADES B. E., Contractive Definitions and Continuity, Contemporary Math.,72(1998), 233-245.