Sentence examples for dominated function from inspiring English sources

In this paper, we introduce the notion of ( g, φ h ) -convex dominated function and present some properties of them.

As studied in Theorem KST, it is more practical to put an assumption on the dominated function ψ than to put one on the mapping T itself.

In the following sections, our main results are given: we introduce the notion of ( g, φ h ) -convex dominated function and present some properties of them.

Proof By the Definition 5 with t = 1 2, x = λ a + ( 1 − λ ) b, y = ( 1 − λ ) a + λ b and λ ∈ [ 0, 1 ], as the mapping f is ( g, φ h ) -convex dominated function, we have that.

Finally, we say that ψ satisfies condition (mathcal{M}) if begin{aligned} int_{0}^{infty} bigl[ log_{2}(1+x) bigr]varphi(x),dx< infty, end{aligned} (2.2) where (varphi(x):=sup_{xleq| y|}|psi | y)), (xgeq0) is named minimum radical dominated function of ψ, and (mathcal{F_{psi}}:={psi_{j,k}:psiinmathcal {M}, j, kin{Bbb{Z}}}) is a Riesz basis for (L^{2}{(mathbb {R})}) with (psi inmathcal{M}).

We used the combination of Gauss and Cauchy (dominated) functions as a profile shape.

18(200261-173, 2002), Kavurmacı et al. (New Definitions and Theorems via Different Kinds of Convex Dominated Functions, 2012) and Özdemir et al. (Two new different kinds of convex dominated functions and inequalities via Hermite-Hadamard type, 2012).

Finally, we present a version of Hermite-Hadamard-type inequalities for ( g, φ h ) -convex dominated functions.

Indeed, the author [25] considered some suitable generalized distances without assuming that the dominated functions possess the lower semicontinuity property.

It should be mentioned that in our results, the dominated functions need not possess the lower semicontinuity property.

In [2], Dragomir et al. proved the following theorem for g-convex dominated functions related to (1.1).