Sentence examples for mappings by using from inspiring English sources

Samreen and Kamran [20] also obtained useful results for such mappings by using the following condition, which is weaker than ((mathcal{P})) ((mathcal{P'})):  for any ({f^{n}x}) in X such that (f^{n}x to yin X) with ((f^{n+1}x,f^{n}x) in E(G)) there exist a subsequence ({f^{n_{k}}x}) of ({f^{n}x}) and (n_{0}inmathbb{N}) such that ((y,f^{n_{k}}x) in E(G)) for all (kgeq n_{0}).

We first establish the sufficient conditions which guarantee the Hölder continuity of a solution mapping to the parametric generalized vector quasi-equilibrium problem with set-valued mappings by using a nonlinear scalarization method.

Question Can one establish the Hölder continuity of a solution mapping to the parametric generalized vector quasi-equilibrium problem with set-valued mappings by using a nonlinear scalarization method?

Next, we define two types of monotone mappings by using the relations ≤ ( I ) and ≤ ( II ).

The purpose of this paper is to find the fixed points of pseudocontractive mappings by using the iterative technique.

Li et al. [19] studied some generalized minimax theorems for set-valued mappings by using a nonlinear scalarization function.

We introduce (mathfrak{fns} -mappings by using the cartesian product with relations on (mathfrak{fns} -mappings

We introduce (mathfrak{fns} -mappings by using a cartesian product with relations on (mathfrak{fns} -mappings estabyish some resusingon fixed points of an (mathfrak{fns})-mapping.

We introduce a modified Ishikawa iterative process for approximating a fixed point of two infinitely nonexpansive self-mappings by using the hybrid method in a Hilbert space and prove that the modified Ishikawa iterative sequence converges strongly to a common fixed point of two infinitely nonexpansive self-mappings.

In addition, Cuffdiff controls for cross-replicate variability and also read-mapping ambiguity by using a model for fragment counts based on the beta negative binomial distribution [ 37].

EDS mappings were collected by using a Cambridge Leica Stereoscan S-360 coupled with INCA Energy Sèrie 200 microanalyser (Oxford Instruments).