Generalized Krasnoselskii-Mann Type Iterations for Two Nonexpansive Mappings in Real Hilbert Spaces
Subject Areas : Application of Game Theory in FinanceSirous Moradi 1 , Najmeh Mohitazar 2
1 - Department of Mathematics, Faculty of science, Lorestan University, Khoramabad 68151-4-4316, Iran
2 - Department of Mathematics, Faculty of science, Arak University, Arak
38156-8-8349, Iran
Keywords:
Abstract :
[1] Bauschke, H.H., Combettes, P.L., Convex Analysis and Monotone Operator Theory in Hilbert Spaces, CMS Books in Mathematics, Springer, New York, 2011.
[2] Bauschke, H.H., Burachik, R.S., Combettes, P.L., Elser, V., Luke, D.R., Wolkowicz, H., (eds.) Fixed-Point Algorithms for Inverse Problems in Science and Engineering, Springer Optimization and Its Applications, 49 Springer, 2011.
[3] Berinde, V., Iterative Approximation of Fixed Points, Lecture Notes in Mathematics, vol. 1912. Springer, Berlin, 2007.
[4] Browder, F. E., Semicontractive and semiaccretive nonlinear mappings in Banach spaces, Bull. Amer. Math. Soc, 1968, 74, P. 661-665. Doi:10.1090/S0002-9904-1968-11979-2
[5] Cegielski, A., Iterative Methods for Fixed Point Problems in Hilbert Spaces: Lecture Notes in Mathematics, 2057. Springer, Berlin, 2012.
[6] Chang, S.S., Cho, Y.J., Zhou, H. (eds.), Iterative Methods for Nonlinear Operator Equations in Banach
Spaces, Nova Science, Huntington, NY, 2002.
[7] Chidume, C.E., Geometric Properties of Banach Spaces and Nonlinear Iterations, Lecture Notes in Mathematics, 1965. Springer, London, 2009.
[8] Chidume, C.E., Chidume, C.O., Iterative approximation of fixed points of nonexpansive mappings, J.
Math. Anal. Appl, 2006, 318, P. 288–295. Doi: 10.1016/j.jmaa.2005.05.023
[9] Cho, Y.J., Kang, S.M., Qin, X., Approximation of common fixed points of an infinite family of nonexpansive mappings in Banach spaces, Comput. Math. Appl, 2008, 56, P. 2058–2064.
Doi: 10.1016/j.camwa.2008.03.035
[10] Combettes, P.L., Solving monotone inclusions via compositions of nonexpansive averaged operators, Optimization, , 2004, 53, P. 475–504. Doi: 10.1080/02331930412331327157
[11] Genel, A., Lindenstrauss, J., An example concerning fixed points Isr. J. Math, 1975, 22, P. 81–86. Doi:10.1007/BF02757276
[12] Hao, Y., Cho, S. Y., Qin, X., Some weak convergence theorems for a family of asymptotically nonexpansive nonself mappings, Fixed Point Theory Appl, Article ID 218573, 2010. Doi:10.1155/2010/218573
[13] Kanzow, C., Shehu, Y., Generalized Krasnoselskii–Mann type iterations for nonexpansive mappings in Hilbert spaces, Comput. Optim. Appl, 2017, 67, P. 595–620. Doi: 10.1007/s10589-017-9902-0
[14] Kim, T.-H., Xu, H.-K., Strong convergence of modified Mann iterations, Nonlinear Anal, 2005, 61, P. 51–60. Doi:10.1016/j.na.2004.11.011
[15] Krasnoselskii, M.A., Two remarks on the method of successive approximations, Uspekhi Mat. Nauk, 1955, 10, P. 123–127. mi.mathnet.ru/umn7954
[16] Liang, J., Fadili, J., Peyré, G., Convergence rates with inexact non-expansive operators, Math. Program, 2016, 159, P. 403–434. Doi: 10.1007/s10107-015-0964-4
[17] Mann, W.R., Mean value methods in iteration, Bull. Am. Math. Soc, 1953, 4, P. 506–510.
Doi: 10.1090/S0002-9939-1953-0054846-3
[18] Opial, Z., Weak convergence of the sequence of successive appproximations for nonexpansive mappings, Bull. Amer. Math. Soc, 1967, 73, P. 591-597. Doi: 10.1090/S0002-9904-1967-11761-0
[19] Reich, S., Weak convergence theorems for nonexpansive mappings in Banach spaces, J. Math. Anal. Appl, 1979, 67, P. 274-276. Doi: 10.1016/0022-247X(79)90024-6
[20] Suzuki, T., A sufficient and necessary condition for Halpern-type strong convergence to fixed points
of nonexpansive mappings, Proc. Am. Math. Soc, , 2007, 135, P. 99–106. www.jstor.org/stable/20534551
[21] Tani, K. K., Xu, H. K., Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. Math. Anal. Appl, 1993, 178, P. 301-308. Doi: 10.1006/jmaa.1993.1309
[22] Xu, H. K., Ori, M. G., An implicit iterative process for nonexpansive mappings, Numer. Funct. Anal. Optim, 2001, 22, P. 767-773. Doi: 10.1081/NFA-100105317
[23] Nasr, N., Farhadi Sartangi, M., Madahi, Z., A Fuzzy Random Walk Technique to Forecasting Volatility of Iran Stock Exchange Index, Advances in Mathematical Finance and Applications, 2019, 4(1), P.15-30.
Doi: 10.22034/amfa.2019.583911.1172