Fixed point iterations of three asymptotically pseudocontractive mappings

• Autorzy: Rafiq A.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we establish the strong convergence for a modified three-step iterative scheme with errors associated with three mappings in real Banach spaces. Moreover, our technique of proofs is of independent interest. Remark at the end simplifies many known results.

Słowa kluczowe

EN

modified three-step iterative scheme; uniformly continuous mapping; L-Lipschitzian mapping; asymptotically pseudocontractive mappings; Banach space

PL

schemat iteracyjny modyfikowany trzyetapowo; odwzorowania ciągłe równomiernie; odwzorowanie L-Lipschitziana; przestrzeń Banacha

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2013
• Tom: Vol. 46, nr 3
• Strony: 559--569
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Rafiq A.

• Hajvery University, 43-52 Industrial Area, Gulberg-III, Lahore, Pakistan

Bibliografia

• [1] R. P. Agarwal, Y. J. Cho, J. Li, N. J. Huang, Stability of iterative procedures with errors approximating common fixed points for a couple of quasi-contractive mappings in q-uniformly smooth Banach spaces, J. Math. Anal. Appl. 272 (2002), 435–447.
• [2] S. S. Chang et al., Some results for uniformly L-Lipschitzian mappings in Banach spaces, App. Math. Lett., doi:10.1016/j.aml.2008.02.016.
• [3] C. E. Chidume, Iterative algorithm for nonexpansive mappings and some of their generalizations, Nonlinear Anal. (to V. Lakshmikantham on his 80th birthday) 1, 2 (2003), 383–429.
• [4] C. E. Chidume et al., Convergence of the Mann iteration algorithm for a class of pseudocontractive mappings, Appl. Math. Comput. 194(1) (2007), 1–6.
• [5] C. E. Chidume, C. O. Chidume, Convergence theorem for zeros of generalized Lipschitz generalized phi-quasiaccretive operators, Proc. Amer. Math. Soc. 134 (2006), 243–251.
• [6] C. E. Chidume, C. O. Chidume, Convergence theorem for fixed points of uniformly continuous generalized phihemicontractive mappings, J. Math. Anal. Appl. 303 (2005), 545–554.
• [7] G. Das, J. P. Debata, Fixed points of quasi-nonexpansive mappings, Indian J. Pure. Appl. Math. 17 (1986), 1263–1269.
• [8] K. Goebel, W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 35 (1972), 171–174.
• [9] S. Ishikawa, Fixed point by a new iteration method, Proc. Amer. Math. Soc. 44 (1974), 147–150.
• [10] L. S. Liu, Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces, J. Math. Anal. Appl. 1945 (1995), 114–125.
• [11] W. R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953), 506–510.
• [12] C. Moore, B. V. Nnoli, Iterative solution of nonlinear equations involving set-valued uniformly accretive operators, Comput. Math. Appl. 42 (2001), 131–140.
• [13] E. U. Ofoedu, Strong convergence theorem for uniformly L-Lipschitzian asymptotically pseudocontractive mapping in real Banach space, Math. Anal. Appl. 321(2) (2006), 722-728.
• [14] B. E. Rhoades, A comparison of various definition of contractive mappings, Trans. Amer. Math. Soc. 226 (1977), 257–290.
• [15] J. Schu, Iterative construction of fixed point of asymptotically nonexpansive mappings, J. Math. Anal. Appl. 158 (1991), 407–413.
• [16] Y. Xu, Ishikawa and Mann iterative process with errors for nonlinear strongly accretive operator equations, J. Math. Anal. Appl. 224 (1998), 98–101.
• [17] B. L. Xu, M. A. Noor, Fixed point iterations for asymptotically nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 267 (2002), 444-453.
• [18] H. K. Xu, Inequalities in Banach spaces with applications, Nonlinear Anal. 16(12) (1991), 1127–1138.