Sentence examples for mappings instead of from inspiring English sources

The purpose of this paper is, by using a simple and quite different method, to study the convergence of implicit iterative sequence defined by (1.12) and (1.16) to a common fixed point for a finite family of -Lipschitzian mappings instead of the assumption that is a uniformly -Lipschitzian and asymptotically pseudocontractive mapping in a Banach space.

A further possible generalization is to consider four mappings instead of two and ascertain analogous common fixed point theorems.

Both above results are based on the topological degree theory for set-valued mappings, instead of the technique of continuous selection.

Based on topological degree for set-valued mappings, instead of the technique of continuous selection, an alternative theorem is obtained which says that the generalized variational inequalities have either a solution or an exceptional family of elements.

Another way is to use the Bregman distance instead of the norm, Bregman (quasi- nonexpansive mappings instead of the (quasi- nonexpansive mappings and the Bregman projectinsteadtead of the metric projection.

Remark 3.1 As an application of exceptional family of elements for set-valued mappings in Isac sense, in Theorem 3.1, we establish the alternative theorem of the existence of a solution for GVI ( F, K ) based on the topological degree for set-valued mappings, instead of the Leray Schauder type alternative and the technique of continuous selection.

Though he did not abandon this idea, later he proposed a generalization of the category of sets (and mappings) instead.

In this article, motivated by Dhompongsa et al.[12], we prove some fixed point theorems for nonspreading mappings for a general Banach space, i.e., nonspreading mappings satisfying (1.2) instead of (1.1).

They therefore suggested to approximate the fixed points of multivalued mappings S directly instead of (P_{S}) and without imposing the strict fixed point set condition on S.

On the other hand Mizoguchi and Takahashi [9] have improved Reich's result [10] and proved the existence of fixed points for multivalued maps in the case when values of mappings are closed bounded instead of compact.

The analytical methods used to process the 15 generated RNA-Seq datasets require the use of single nucleotide activities instead of read mappings.