Recurrent Inequalities and Some of their Applications to Picard and Mann Iterations
By: Vasile Berinde and Ştefan Măruşter
References
- [1] Ya.I.Alber, On the solution of equations and variational inequalities with maximal monotone operators, Soviet mathematics Doklady, 20, (1979), 871-876
- [2] Ya.I.Alber, C.E.Chidume, and H.Zegeye, Approximationg fixed points of total asymptotically nonexpansive mappings, Fixed Point Theory and Appl., 2006, Article ID 10673
- [3] G.V.R.Babu and K.N.V.V.Vara Prasad, Mann iteration converges faster than Ishikawa iteration for the class of Zamfirescu operators, Fixed Point Theory and Ap- plications, (2006), Article ID 49615
- [4] V.Berinde, Approximating fixed points of weak contractions using the Picard iterations, Nonlinear Analysis Forum, (2004)
- [5] V.Berinde, Iterative approximation of fixed points, Lecture Notes in Mathematics, (2007)
- [6] V.Berinde, On a family of first order difference inequalities used in the iterative approximation of fixed points, Creative Math. and Inf., 18, (2009), 110-122
- [7] V.Berinde, A note on a difference inequality used in the iterative approximation of fixed points, Creative Math. and Inf., 18, (2009), 6-9
- [8] D.Boonchari and S.Saejung, Construction of common fixed points of a countable family of λ-demicontractive mappings in arbitrary Banach spaces, Appl. Math.Comput., 216, (2010), 173-178
- [9] C.E.Chidume, M.Abbas, and B.Ali, Convergence of the Mann iteration algorithm for a class of pseudocontractive mappings, Appl. Math. Comput., 194, (2007), 1-6
- [10] L.Ciric, A.Rafiq, S.Radenovic, M. Rajovic, and J.S.Ume, On Mann implicit iteration for strongly accretive and strongly pseudo-contractive mappings, Appl.Math. Comput., 198, (2008), 128-137
- [11] W.G.Dotson, An iterative process for nonlinear monotonic nonexpasive operators in Hilbert space, Mathematics of Computation, 32, (1978), 223-225
- [12] A.Genel and J.Lindenstrauss, An example concerning fixed points, Israel J. Math- ematics, 22, (1975), 81-86
- [13] T.L.Hicks and J.D.Kubicek, On the Mann iteration process in a Hilbert spaces, J. Math. Anal. Appl., 59, (1977), 489-504
- [14] S.M.Kang, A.Rafiq, and N.Hussain,Weak and strong convergence of fixed points of demicontractive mappings in smooth Banach spaces, Int. J. Pure Appl. Math., 84, (2013), 251-268
- [15] Liwei Liu, Proc. Amer. Math. Soc., 125, (1997), 1363-1366
- [16] St.Maruster, Sur le calcul des zeros d'un operateur discontinu par iteration, Canad.Math. Bull., 16, (1973), 541-544
- [17] St.Maruster, The solution by iteration of nonlinear equations in Hilbert spaces, Proc. Amer. Math.Soc., 63, (1977), 69-73
- [18] A.M.Ostrowski, The round-of stability of iterations, Zeitschrift für angewandte mathematik und mechanik, 47, (1967), 77-81
- [19] Y.Qing and B.E.Rhoades, T-stability of Picard iteration in metric spaces, Fixed Point Theory and Applications, 2008, Article ID418971
- [20] D.R.Sahu and A.Petrusel, Strong convergence of iterative methods by strictly pseudocontractive mappings in Banach spaces, Nonlinear Analysis, 74, (2011), 6012-6023
- [21] M.De la Sen, Some combined relations between Contractive mappings, Kannan mappings, Reasonable Expansive mappings, and T-stability, Fixed Point Theory and Applications, (2009), Article ID815637
- [22] K.K.Tan and H.K.Xu, Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. Math. Anal. Appl., 178, (1993), 301-308
Language: English
Page range: 3 - 16
Submitted on: Jun 16, 2014
Accepted on: Jul 30, 2014
Published on: Dec 11, 2014
Published by: West University of Timisoara
In partnership with: Paradigm Publishing Services
Publication frequency: Volume open
Related subjects:
© 2014 Vasile Berinde, Ştefan Măruşter, published by West University of Timisoara
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.