Sentence examples for mappings in certain from inspiring English sources

Some authors studied the convergence of iteration process (1.8) for nonexpansive mappings in certain Banach spaces (see [5, 10]).

Takahashi [17] proved a strong convergence theorem of the following iterative algorithm for countable families of nonexpansive mappings in certain Banach spaces: x n + 1 = t n f x n + ( 1 − t n ) T n x n, n ∈ N. (1.9).

Likewise, the SNP-tolerance feature implemented in our program should help resolve mappings in certain genomic regions.

In this paper, we introduce several types of viscosity approximation methods for nonexpansive nonself-mappings in certain Banach spaces.

Using new analysis techniques, we prove several strong convergence theorems for nonexpansive nonself-mappings in certain Banach spaces without boundary conditions.

Using these results, they proved two strong convergence theorems for nonexpansive nonself-mappings in certain Banach spaces without any boundary conditions.

Suzuki [16] established a strong convergence theorem by using Halpern's method to averaged mapping T λ = λ I + ( 1 − λ ) T, λ ∈ ( 0, 1 ) for nonexpansive mappings T in certain Banach spaces.

Readers may consult [11, 25, 26] for the convergence of Ishikawa iteration sequences for nonexpansive mappings and nonexpansive semigroups in certain Banach spaces.

Investigation of the existence and uniqueness of fixed points of certain mappings in the framework of metric spaces is one of the centers of interests in nonlinear functional analysis.

Some relations between such concepts subject either to sufficient, necessary, or necessary and sufficient conditions are obtained so that in certain self-mappings can exhibit combined properties being inherent to each of its various characterizations.

In nonlinear functional analysis, the study of fixed points of given mappings satisfying certain contractive conditions in various abstract spaces has been at the center of vigorous research activity in the last decades.