Sentence examples for in satisfying condition from inspiring English sources

Let be sequences in satisfying condition (ii) in Theorem 3.2.

where is a sequence in and in satisfying conditions and.

where is a sequence in and in satisfying conditions.

Let,,,, and be six sequences in satisfying conditions: (1) for.

Let be a sequence in satisfying conditions and.

Let,,,, and be six sequences in satisfying conditions (1)–(3) of Theorem 3.6.

Let be a sequence in satisfying conditions and and let be a strongly regular matrix.

for all, where,, are three sequences in, and is a sequence in satisfying conditions (i)–(iii) and (v).

Let μ be a measure of noncompactness in E satisfying condition (m).

Let f be a contraction of C into itself with constant α ∈ ( 0, 1 ), let { α n } n = 1 ∞, { β n } n = 1 ∞ and { γ n } n = 1 ∞ be sequences in ( 0, 1 ) satisfying conditions (C1 - C4), and let { δ n } n = 1 ∞ be a sequence in ( 0, 1 ) satisfying condition ( C 5 ′ ).

Example 4.6 Let C be a compact convex subset of a smooth Banach space E such that 0 ∈ C. Let f be a contraction of C into itself with constant α ∈ ( 0, 1 ), let { α n } n = 1 ∞, { β n } n = 1 ∞ and { γ n } n = 1 ∞ be sequences in ( 0, 1 ) satisfying conditions (C1 - C4), and let { δ n } n = 1 ∞ be a sequence in ( 0, 1 ) satisfying condition ( C 5 ′ ).