Sentence examples for ordered functions from inspiring English sources

Proof Since f and w are similarly ordered functions, the proof follows from Theorem 3.10.

Then their product fg is also a generalized ((alpha,m -preinvex function provided thalpha,m -preinvexilarly ordered functions with (fggeq0).

Property 4 Let f and g be similarly ordered functions on I, i.e., ( f ( x ) − f ( y ) ) ( g ( x ) − g ( y ) ) ≥ 0 (2.2). for all x, y ∈ I.

Then the product of f and w will be a relative semi-convex function if f and w are similarly ordered functions.

In this section, it will be introduced the notations and definitions needed forward together with some auxiliary functions useful to construct some ordered functions on the basis of the not necessarily ordered lower and upper solutions of the referred problem.

They are ordered function of epicentral distance, with distance increasing from up to down.

The library provides parallel map and fold (reduce) higher order functions and targets standard cache coherent shared memory multi-cores.

Let us make use of function (rho ^{m_{i}}_{f_{i}}(x_{i})) to define the following social ordering function: Social ordering function 1.

Open image in new window Fig. 1 Social ordering function ( mathbf{R } ^{ lex }_{rho }).

Thereafter, second-order functions became a ubiquitous feature of modern logic and semantic analysis.

It pointedly noted, "The United Nations cannot assume law and order functions which are properly the responsibility of the government of Lebanon".