Sentence examples for m is semicompact from inspiring English sources

If ∑ m = 1 N δ m T m is semicompact, then { x n } converges strongly to some point in F.

In Theorem 3.1 in [8], if there exists some positive integer m such that S m is semicompact, then { x n } converges strongly to x ¯ ∈ Π 3.

If ∑ m = 1 N δ m T m is semicompact, then { x n } converges strongly to some point in F. Proof Since ∑ m = 1 N δ m T m is semicompact, we see that there exists a subsequence { x n i } of { x n } such that x n i → x ∗.

In addition, if there exists some positive integer m such that S m is semicompact, then { x n }, { y n } converge strongly to a point x ¯ ∈ Γ = { x ∈ C, A x ∈ Q }.

If ∑ m = 1 N δ m T m is semicompact, then { x n } converges strongly to some point in F. In Hilbert spaces, we find from Theorem 2.1 the following.

Recall that the mapping T : K → K is semicompact if any sequence { x n } in K satisfying lim n → ∞ ∥ x n − T x n ∥ = 0 has a convergent subsequence.

Then F f, T) ≠ ∅ if one of the following conditions holds: (a): cl(T(M)) is compact and f and T are continuous; (b): wcl(T(M)) is weakly compact, f is weakly continuous and (f - T) is demiclosed at 0; (c): T(M) is bounded, T is semicompact and f and T are continuous; (d): T(M) is bounded, T is weakly semicompact, f is weakly continuous and (f - T) is demiclosed at 0. Proof.

Since M is inner semicompact at ((hat{x},hat{y})), for the above ((x_{k},y_{k})), there exists a sequence of (z_{k}in M x_{k},y_{k})) that contains a subsequence converging to some ẑ.

If M is inner semicompact at ((hat{x},hat{y})), then, for any (y^in Y^) satisfying (sup_{sin Ssetminus{0}} frac {langle y^,srangle}{|s|}=:v<0), D_{M}^N hat{x},hat{y}) bigl y^ bigr)subsetbigcup _{hat{z}in M hat{x},hat {y})}F hat{z})^y^+N hat{x},K).

(8)   (ii) If M is inner semicompact at ((hat{x},hat{y})), then, for any (y^in Y^), D^G(hat{x},hat{y}) bigl y^ bigr)subsetbigcup _{hat{z}in M hat{x},hat {y})}F hat{z})^y^+N hat{x},operatorname{dom}G).

If M is inner semicompact at ((hat{x},hat{y})), then, for any (y^in Y^), D^G(hat{x},hat{y}) bigl y^ bigr)subsetbigcup _{hat{z}in M hat{x},hat {y})}F hat{z})^y^+N hat{x},operatorname{dom}G).