Sentence examples for satisfying properties from inspiring English sources

Let X be a Banach space endowed with a family of seminorms ({R_{k}( cdot) }) satisfying properties 1-4 staboveandve, and (|!|!|cdot|!|!|) be the equivalent norm given above.

Suppose that a differential equation for λ ( x, φ ) satisfying properties (1) and (2) has been found and that a priori the function u 0 e, which represents the exact data of IGP related to a function λ depending only on x, is known.

From up-to-now considerations we conclude that for each (varepsilon >0), there exist (deltain 0,varepseeon/2)) (see Part 2 of the proof of Lemma 6) and continuous functions (g^{varepsilon}:[0,1]to S) and (h^{varepsilon}:Stomathbb{R}^{n}) satisfying properties (iv - vii).

Corollary 2.5 Let A and B ∗ be class A operators satisfying property.

Suppose that A and B ∗ are class A operators satisfying property.

Theorem 2.4 Let A and B ∗ be class A operators satisfying property.

Chugh et al. [15] obtained some fixed point results for maps satisfying property P in G-metric spaces.

While, Chugh et al. [9] obtained some fixed point results for maps satisfying property p in G-metric spaces.