Sentence examples for which is continuous on from inspiring English sources

Let (mathcal{F}={T_{t}; tgeq0}) be a one-parameter semigroup of mappings from C into M which is continuous on C. Let A be a dense subset of ([0,+infty)). Then we have operatorname{Fix}(mathcal{F}) = bigcap_{a in A} operatorname{Fix}(T_{a}).

Let (mathcal{F}={T_{t}; tgeq0}) be a one-parameter semigroup of mappings from C into M which is continuous on C. Let α and β be two positive real numbers such that (frac{alpha}{beta}) is irrational, then we have operatorname{Fix}(mathcal{F}) = operatorname{Fix}(T_{alpha}) cap operatorname{Fix}(T_{beta}).

Let (mathcal{F}={T_{t}; tgeq0}) be a one-parameter semigroup of nonexpansive mappings from C into M which is continuous on C. Let α and β be two positive real numbers such that (frac{alpha}{beta}) is irrational, then we have operatorname{Fix}(mathcal{F}) = operatorname{Fix} bigl(lambda T_{alpha}+ (1-lambda)T_{beta}bigr) for any (lambdain 0,1)).

which is continuous on [ 0, a ].

Let (A Dto Y) be a quasilinear operator which is continuous on line segments.

provided f satisfies (3.1) and is Riemann integrable (or sufficiently, convex on [ a, b ] ), which is continuous on [ a, b ].

Here C ( J ) denotes the set of real functions which are continuous on the interval J.

C E [ a, b ] is the space of fuzzy-valued functions which are continuous on [ a, b ].

We are especially interested in specifying the structure of general linear two-point boundary conditions guaranteeing existence and uniqueness of solutions which are continuous on a closed interval including the singular point.

Let (mathcal{B}) be the set of all functions (phi:(-infty,0]times -infty,0]times -infty) which are continuous on ([-alpha,0]rightarrowa,0]), (alpha,bEtageq0), whichthe seminorm |phi|_{marecontinuousp_{(s,t)in[-alpha,0]times[-beta,0]} bigl| phi(s,t)bigr|.

⧫ L p E ( a, b ), 1 ≤ p ≤ ∞ is the set of all fuzzy-valued measurable functions f on [ a, b ] where ∥ f ∥ p = ( ∫ 0 1 ( d ( f ( t ), 0 ) ) p d t ) 1 p. ⧫ C E [ a, b ] is a space of fuzzy-valued functions, which are continuous on [ a, b ]. ⧫ C n E [ a, b ] indicates the set of all fuzzy-valued functions, which are continuous up to order n.