On Boyd-Wong-type fixed point results
Authors: Aranđelović Ivan D
Keywords: fixed point; Picard iterates; symmetric space
Abstract:
This talk (paper) gives a survey of recent results in the theory of Boyd-Wong-type contractions and its aim is to present a simple and unified treatment to this theory. In final part of paper, we present one recent fixed point result for Boyd-Wong-type contractions defined on symmetric spaces.
References:
[1] Aranđelović, I.D., Kečkić, D.J. (2012) Symmetric spaces approach to some fixed point results. Nonlinear Analysis: Theory, Methods & Applications, 75(13): 5157-5168
[2] Bianchini, R.M., Grandolfi, M. (1968) Transformazioni di tipo contracttivo generalizzato in uno spazio metric. Atti Accad. Naz. Lincei, Ser. Rend. Cl. Sci. Fis. Mat. Natur, VII, 45, 212-216
[3] Boyd, D.W., Wong, J.S.W. (1969) On nonlinear contractions. Proceedings of the American Mathematical Society, 20(2): 458-458
[4] Browder, F.E. (1968) On the Convergence of Successive Approximations for Nonlinear Functional Equations. Indagationes Mathematicae (Proceedings), 71: 27-35
[5] Hicks, T.L., Rhoades, B.E. (1979) A Banach type fixed point theorem. Math. Japonica, 327-330; 24
[6] Jachymski, J., Matkowski, J., Wiatkowski, T.S. (1995) Nonlinear contractios on semimetric spaces. J. Appl. Anal., 125-134; 1
[7] Rhoades, B.E. (1983) Contractive definitions revisited: Topological methods in non-linear analysis. Contemporary Mathematics, AMS, 21, 189-205
[8] Rus, I. (1983) Generalized contractions. ‘Babes-Bolyai’ University, Faculty of Mathematics, Reasrch Seminaries, Seminary on Fixed Point Theory, Preprint, nr. 3, 1-1130
[9] Zitarosa, A. (1968) Na generalizzatione del teorema di Banach sulle contrazioni. Mathematicae, 23, 417-424