zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
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.
47J25Iterative procedures (nonlinear operator equations)
47H09Mappings defined by “shrinking” properties
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
Full Text: DOI
[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. (2002) · Zbl 1070.47054
[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, No. 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, No. 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, No. 2, 135-151 (2008) · Zbl 1223.47095