Sentence examples for be two maps such from inspiring English sources

Let f : X → Y, g : Y → Z be two maps such that g ∘ f : X → Z is sb-closed map.

Let ( X, ⪯, d ) be a partially ordered metric space; f, g : X × X ⟶ X be two maps such that 1. X is complete;   2.

Let be a nonempty subset of a reflexive Banach space and be two maps such that is weakly closed in and.

Let be two maps such that there exists with the following properties: (P1) and for every ; (P2) there exists such that for every, with, and, where ; (P3) there exists such that for all and one has (3.3).

Let (( X,d ) ) be a dislocated quasi-b-metric space with (s>1) and let (f,g Xrightarrow X) be two maps such that (f ( X ) subseteq g ( X )) and one of these two subsets of X is (dqb -complete.

Then for all n ∈ N, the pair ( f n, f n ) has the mixed weakly monotone property on X. Theorem 2.1 Let ( X, ⪯, S ) be a partially ordered S-metric space; f, g : X × X ⟶ X be two maps such that 1. X is complete;   2.

Definition 1 A crossed system of monoids is a quadruple ( A, B, α, f ), where A and B are two monoids, and f : B × B → A and α : B → End ( A ), where End ( A ) denotes the collection of endomorphism of A, are two maps such that the following conditions hold: (1).

Assume that (Ecolon N rightarrow N ) and (Fcolonmathbb {R}rightarrowmathbb{R} ) are two maps such that (F(f(b)+a)=f(E(b))+a ) for each non-negative real number a. Suppose that (lbrace f_{j}, jin I rbrace ) is a family of real-valued functions defined on a GSEC set (Bsubseteq N ) which are bounded from above.

Let M be a nonempty bounded closed convex subset of a Hilbert space X and let A, B be two maps from M into X such that (i) A is weakly-strongly continuous;   (ii) B is a nonexpansive mapping;   (iii) A x + B x ∈ M for all x ∈ M.  .

Lemma 3.2 Let M be a nonempty bounded closed convex subset of a Banach space X and let A, B be two maps from M into X such that (i) A is weakly-strongly continuous;   (ii) B is nonexpansive;   (iii) A x + B x ∈ M for every x ∈ M.  .

It asserts that, if M is a nonempty, bounded, closed, and convex subset of a Banach space X and A, B are two maps from M into X such that (A(M +B(M subseteq M), A is compact and B is a contraction, then (A+B) has at least one fixed point in M (see [1] or [2], p.31).