Sentence examples for mappings and is from inspiring English sources

If at least one mapping of the mappings and is semicompact, then the implicitly iterative sequence defined by (1.2) converges strongly to a common fixed point of and.

In what follows, unless other specified, for each, we always suppose that is a Hilbert space with norm denoted by,, are single-valued mappings, and is a nonlinear mapping.

We prove the theorem under the hypothesis that neither of the mappings and is necessarily a self-mapping.

where is strongly positive defined by (1.15), is a countable family of nonexpansive mappings, and is an -contraction.

Let, is a -quasicontraction that commutes with, one of the mappings and is continuous, and they satisfy.

(2) Theorems 2.7 2.16 represent very strong variants of the results in [3, 8, 11, 13] in the sense that the commutativity or compatibility of the mappings and is replaced by the hypothesis that is a Banach operator pair, needs not be linear or affine, and needs not be -nonexpansive.

Let be a sequence of set-valued mappings and be a set-valued mapping.

Let be an -Lipschitzian semigroup of pseudocontractive mappings and be an -Lipschitzian -strongly pseudocontractive mapping.

Let the mapping be such that for each, the mappings and are upper semicontinuous with nonempty compact values and.

Mappings and are called -compatible if whenever and.

For all the mappings and are Fréchet-differentiable at.