Sentence examples for map f and from inspiring English sources

Cabada and Pouso [3] considered also a Carathéodory map f, and they established the existence of a solution to the problem with Neumann or periodic boundary conditions.

In this subsection we collect some further results on the relationship between fractional differences of a map f and associated properties of f itself.

We can easily prove that [ 0, 1 2 ] is a transitive set of ( X, f 1, ∞ ). Figure 1 and Figure 2 denote the tent map f and the 2nd iterate f 2 of the tent map f, respectively.

If ( h 1, ⋯, h t ) is a right C -factorization of a map f, and f i = h 1 ⋯ h i for 0 ≤ i ≤ t, then η C Y ( f t ) ⊂ ⋯ ⊂ η C Y ( f 1 ) ⊂ η C Y ( f 0 ) = Hom ( C, Y ) is a chain of proper inclusions of submodules and any such chain is obtained in this way.

(S_{r}), after which the dynamics of the slow flow governs the drift towards T. It defines two maps x_{T} = varepsilon F(x_{S},sqrt{varepsilon },A),qquad x_{T} = varepsilon B(x_{S},sqrt {varepsilon },A), (26) where the forward map F and the backward map B are known to be smooth in terms of ((x_{S},sqrt{varepsilon },A)); see [19].

Then (Phi =f_* circ f^*) is a monad on ({text {Coh}}(Y))—that is, a comonad on the opposite category ({text {Coh}}(Y)^o), We then have ({text {Coalg}}({text {Coh}}(Y)^o,Phi ^o) cong {text {Coh}}(Y')^o), where Open image in new window is the Stein factorization of the map f, and we have (Psi cong f'_*).

Now, we introduce the concept of compatible mapping for a trivariate mapping F and a self-mapping g akin to compatible mapping as introduced by Choudhary and Kundu [11] for a bivariate mapping F and a self-mapping g.

This manuscript has two aims: first we extend the definitions of compatibility and weakly reciprocally continuity, for a trivariate mapping F and a self-mapping g akin to a compatible mapping as introduced by Choudhary and Kundu (Nonlinear Anal. 73:2010-2531, 2010) for a bivariate mapping F and a self-mapping g.

Let f,g,R,S X→X be four mappings such that f(X)⊆R(X) and g(X)⊆S X) and dominating maps f and g are weak annihilators of R and S, respectively.

Clearly, commuting maps f and T weakly commute.

Hence, the maps F and g have a coupled coincidence point.