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Convergence theorem for fixed points of nearly uniformly \(L\)-Lipschitzian asymptotically generalized \(\Phi \)-hemicontractive mappings. (English) Zbl 1239.47055
From the summary: We introduce the new class of asymptotically generalized \(\Phi\)-hemicontractive mappings and establish a strong convergence theorem for the iterative sequence generated by these mappings in a general Banach space.

MSC:
47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H10 Fixed-point theorems
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[1] Alber, Ya.I.; Chidume, C.E.; Zegeye, H., Regularization of nonlinear ill-posed equations with accretive operators, Fixed point theory appl., 1, 11-33, (2005) · Zbl 1095.47024
[2] Chidume, C.E.; Chidume, C.O., Convergence theorems for fixed points of uniformly continuous generalized \(\Phi\)-hemi-contractive mappings, J. math. anal. appl., 303, 545-554, (2005) · Zbl 1070.47055
[3] Huang, Z., Equivalence theorems of the convergence between Ishikawa and Mann iterations with errors for generalized strongly successively \(\Phi\)-pseudocontractive mappings without Lipschitzian assumptions, J. math. anal. appl., 329, 935-947, (2007) · Zbl 1153.47307
[4] Liu, Z.; Kim, J.K.; Kim, H.K., Convergence theorems and stability problems of the modified Ishikawa iterative sequences for strictly successively hemicontractive mappings, Bull. Korean math. soc., 39, 455-469, (2002) · Zbl 1036.47045
[5] Chang, S.S.; Cho, Y.J.; Zhou, H., Iterative methods for nonlinear operator equations in Banach spaces, ISBN: 1-59033-170-2, (2002), Nova Science Publishers, Inc. Huntington, NY, xiv+459 pp
[6] Chidume, C.E.; Chidume, C.O., Convergence theorem for zeros of generalized Lipschitz generalized phi-quasi-accretive operators, Proc. amer. math. soc., 134, 243-251, (2006) · Zbl 1072.47062
[7] Gu, F., Convergence theorems for \(\phi\)-pseudocontractive type mappings in normed linear spaces, Northeast math. J., 17, 3, 340-346, (2001) · Zbl 1064.47066
[8] Moore, C.; Nnoli, B.V., Iterative solution of nonlinear equations involving set-valued uniformly accretive operators, Comput. math. appl., 42, 131-140, (2001) · Zbl 1060.47511
[9] S.S. Chang, Y.J. Cho, J.K. Kim, Some results for uniformly \(L\)-Lipschitzian mappings in Banach spaces, Appl. Math. Lett., doi:10.1016/j.aml.2008 · Zbl 1163.47308
[10] Ofoedu, E.U., Strong convergence theorem for uniformly \(L\)-Lipschitzian asymptotically pseudocontractive mapping in a real Banach space, J. math. anal. appl., 321, 722-728, (2006) · Zbl 1109.47061
[11] Sahu, D.R., Fixed points of demicontinuous nearly Lipschitzian mappings in Banach spaces, Comment. math. univ. carolin, 46, 4, 653-666, (2005) · Zbl 1123.47041
[12] Goebel, K.; Kirk, W.A., A fixed point theorem for asymptotically nonexpansive mappings, Proc. amer. math. soc., 35, 171-174, (1972) · Zbl 0256.47045
[13] Chang, S.S., Some results for asymptotically pseudocontractive mappings and asymptotically nonexpansive mappings, Proc. amer. math. soc., 129, 845-853, (2001) · Zbl 0968.47017
[14] Chang, S.S., On chidume’s open questions and approximation solutions of multi-valued strongly accretive mapping equation in Banach spaces, J. math. anal. appl., 216, 94-111, (1997) · Zbl 0909.47049
[15] Osilike, M.O.; Aniagbosor, S.C., Weak and strong convergence theorems for fixed points of asymptotically nonexpansive mappings, Math. computer modelling, 32, 1181-1191, (2000) · Zbl 0971.47038
[16] Sahu, D.R.; Beg, Ismat, Weak and strong convergence of fixed points of nearly asymptotically nonexpansive mappings, Internat. J. modern math., 3, 2, 135-151, (2008) · Zbl 1223.47095
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