Sentence examples for instead of g from inspiring English sources

We note that g T ( A, B ) = g T ˜ ( A, B ) / Δ 2. We write g instead of g T ˜.

On the other hand, we repeat the above proof with − g ′, instead of g, we can get (3.3).

Throughout the rest of the paper, we shall use the notation gx instead of g ( x ), where g : X → X and x ∈ X, for brevity.

Let (varepsilon^{q}=1/q), (qinmathbb{N}), and let (g^{q}), (h^{q}) be functions meeting properties (iv - vii) (wiv - viivarepsilon}), (h^{varepsilon}) instead of g, h, respectively).

Since (27) has a ratio based on the g 4 max instead of g 4 max –g 4 min, the disparity of the effect of approximate value is reduced.

For notation simplicity lets represent it as G(V c, E c, t), instead of G (V c, E t c ) and note that G(V c, E c) = G(V c, E c, 0).

For some explicit purposes, it could be more convenient to work directly with g ab, instead of ε g ab, and with the d-metric (Equation 101) which is a particular case of Equation 30 (when h ab =g ab ).

We denote by D τ, σ ( u τ ) the set of all global weak solutions (defined for all t ≥ τ) of the problem (1.1) with data (f σ, g σ ) instead of (f, g) such that u = u τ.

Theorem 45 If, instead of G-continuity of F in the theorem above, we assume that X is ordered complete, then F has a coupled fixed point.

Theorem 4.6 If in the above theorem, instead of G-continuity of F, we assume that X is ordered complete, then F has a coupled fixed point.

Recently, in [19 21], the author established common coupled fixed point theorems by using (g- monotone property instead of (g- monotonenotone property.