zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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)
The equivalence between the convergences of multi-step iterations with errors for uniformly generalized Lipschitz continuous operators. (Chinese) Zbl 1223.47088
Summary: In this paper, the equivalence of the convergence of modified Mann iterations and multi-step Noor iterations with errors is investigated for uniformly generalized Lipschitz continuous and successively asymptotically 𝛷-strongly pseudo-contractive type operators in uniformly smooth Banach spaces. Z.-Y. Huang [J. Math. Anal. Appl. 329, No. 2, 935–947 (2007; Zbl 1153.47307)] showed the equivalence of the convergence criteria between modified Mann and Ishikawa iterations with errors for successively 𝛷-strongly pseudo-contractive operators with bounded range in uniformly smooth Banach spaces. The results obtained in this paper generalize the results of Huang and give an affirmative answer to the conjecture raised by B. E. Rhoades and Ş. M. Şoltuz [Int. J. Math. Math. Sci. No. 7, 451–459 (2003; Zbl 1014.47052)].
MSC:
47J25Iterative procedures (nonlinear operator equations)
47H09Mappings defined by “shrinking” properties
47H10Fixed point theorems for nonlinear operators on topological linear spaces