Sentence examples for mappings one of from inspiring English sources

Utilizing this theorem, we also design an iterative process for finding a common fixed point of two mappings, one of which is an asymptotically strict pseudocontractive mapping in the intermediate sense and the other taken from the more general class of Lipschitz pseudocontractive mappings.

In the following theorem, we introduce an iterative process that converges strongly to a common fixed point of two mappings, one of which is an asymptotically κ-strict pseudocontractive mapping in the intermediate sense with sequence {γ n } and the other Lipschitz continuous and pseudocontractive.

Inspired by [2, 5, 6], the purpose of this paper is to study a family of commuting nonexpansive mappings, one of which is weakly contractive, in arbitrary complete metric spaces and Banach spaces.

where f : C → C is a contractive mapping with α ∈ ( 0, 1 2 ) and { S n }, { T n } are sequences of nonexpansive mappings, one of them is a strongly nonexpansive sequence.

Assume the following conditions are satisfied: (a) the pairs ((S,A)) and ((T,B)) are commutative mappings;   (b) one of S, T, A, and B is continuous.  . the pairs ((S,A)) and ((T,B)) are commutative mappings; one of S, T, A, and B is continuous.

Then for any commuting family S of nonexpansive self-mappings of E, the set F(S) of common fixed points of S is a nonempty nonexpansive retract of E. The object of this paper is to extend Theorems 1.3 and 1.4 for a commuting family S of nonexpansive mappings one of which is multivalued.

A family of commuting nonexpansive self-mappings, one of which is weakly contractive, are studied.

Some common fixed point results for two self-mappings, one of them being a generalized weakly G-contraction of type A and B with respect to the other mapping, are stated in [9].

After that, as an important generalization of nonexpansive mappings, strictly pseudo-contractive mappings become one of the most interesting studied classes of nonexpansive mappings (see, e.g., [19 22]).

For the example of a one-parameter continuous semigroup of nonexpansive mappings, one can see [18].

On the other hand, from the nonexpansivity of the mappings, one sees that (3.24).