Fixed point theorems using diameters of level sets and the notion of R.G.I. mapping

• Autorzy: Akkouchi M.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we generalize and improve a recent result established by W. A. Kirk and L. M. Saliga (see [3], Theorem 4.3, p. 149) by using a result of W. Walter (see [4]). Indeed, We prove that the conclusions of Kirk-Saliga theorem are not only satisfied but, moreover, they are equivalent for a wide class of contractive gauge functions. Our main result contains also a new equivalent conclusion (see Property (4) in Theorem 2.2 below). As a consequence, we recapture (and improve the results of) a theorem proved by M. Angrisani and M. Clavelli in [2]. Theorem 2.2 completes and improves the main result of[1].

Słowa kluczowe

EN

fixed point; level sets; Picard sequences

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2002
• Tom: Vol. 35, nr 3
• Strony: 621--628
• Opis fizyczny: Bibliogr. 4 poz.

Twórcy

autor

Akkouchi M.

• Département de Mathématiques, Faculté des Sciences-Semlalia, Université Cadi Ayyad, Boulevard du Prince My. Abdellah. B.P. 2390, Marrakech, Maroc (Morocco)

Bibliografia

• [1] M. Akkouchi, On a result of W. A. Kirk and L. M. Saliga, J. Comput. Appl. Math. 142(2) (2002), 445-448.
• [2] M. Angrisani, M. Clavelli, Synthetic approaches to problems of fixed points in metric space, Ann. Mat. Pura Appl. (IV) CLXX (1996), 1-12.
• [3] W. A. Kirk and L. M. Saliga, Some results on existence and approximation in metric fixed point theory, J. Comput. Appl. Math. 113 (2000), 141-152.
• [4] W. Walter, Remarks on a paper by F. Browder about contractions, Nonlinear Anal. TMA 5 (1981), 21-25.