Sentence examples for mappings and it from inspiring English sources

Puri and Ralescu in [4] introduced H-derivative (differentiability in the sense of Hukuhara) for fuzzy mappings and it is based on the -difference of sets, as follows.

Recently, Chen and Li [4] introduced the class of Banach operator pairs as a new class of noncommuting mappings and it has been further studied by Hussain [5], Khan and Akbar [16], and Pathak and Hussain [14].

Finding the fixed points of nonexpansive mappings is an important topic in the theory of nonexpansive mappings, and it has wide applications in a number of applied areas such as the convex feasibility problem [1 3], the split feasibility problem [4], image recovery and signal processing [5].

Remark 3.2 Theorem 3.1 extends the main results in [4, 16, 18, 20] to the case of asymptotically nonexpansive in the intermediate sense mappings and it seems to be new even in the case that the space has a Fr échet differentiable norm.

However, for applications (numerical analysis, optimization, etc). it is important to consider functions that are not self-mappings, and it is natural to search for sufficient conditions which would guarantee the existence of fixed points for such mappings.

Subsequently, Nieto and López [5] extended this result for nondecreasing mappings and applied it to obtain a unique solution for a first-order ordinary differential equation with periodic boundary conditions.

Subsequently, Nieto and Rodríguez-López [16] extended the result of [15] for nondecreasing mappings and applied it to obtain a unique solution for a first-order ordinary differential equation with periodic boundary conditions.

Subsequently, Nieto and Rodríguez-López [7] extended this result for nondecreasing mappings and applied it to obtain a unique solution for a first-order ordinary differential equation with periodic boundary conditions.

Subsequently, Nieto et al. [18] extended this result in [17] for non-decreasing mappings and applied it to obtain a unique solution for a first-order ordinary differential equation with periodic boundary conditions.

In this article, we define a tangential property which can be used not only for single-valued mappings but also for multi-valued mappings, and used it in the prove for the existence of a common fixed point theorems of Gregus type for four mappings satisfying a strict general contractive condition of integral type in metric spaces.

Subsequently, Nieto and Rodríguez-López [25] used the contractive condition begin{aligned} d(mathcal F x,mathcal F y)le kd x,y quad text{ for}quad ypreceq x. end{aligned} (1.1 where (kin [0,1)) and extended this result for nondecreasing mappings and applied it to obtain a unique solution for a first order ordinary differential equation with periodic boundary conditions.