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}).
Dominating functions in the molecular signature.
Furthermore, we also discuss the results with the lower semicontinuities of the dominated functions in place of the original orbital continuities of the mappings.
In this paper, we introduce the notion of ( g, φ h ) -convex dominated function and present some properties of them.
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.
It should be mentioned that in this paper we remove the lower semicontinuity property of the dominated functions in Caristi-type cyclic maps.
The problem is that form (kata) dominates function and purpose (jitsu) in every nook and cranny of Japanese life.
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.
