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Abstract  

Given a multiobjective optimization problem with the components of the objective function as well as the constraint functions being composed convex functions, we introduce, by using the Fenchel-Moreau conjugate of the functions involved, a suitable dual problem. Under a standard constraint qualification and some convexity as well as monotonicity conditions we prove the existence of strong duality. Finally, some particular cases of this problem are presented.

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Abstract  

This study utilized artificial neural network (ANN) to explore the nonlinear influences of firm size, profitability, and employee productivity upon patent citations of the US pharmaceutical companies. The results showed that firm size, profitability, and employee productivity of the US pharmaceutical companies had the nonlinearly and monotonically positive influences upon their patent citations. Therefore, if US pharmaceutical companies want to enhance their innovation performance, they should pay attention on their firm size, profitability, and employee productivity.

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Abstract  

Insertion of lattice-valued functions in a monotone manner is investigated. For L a ⊲-separable completely distributive lattice (i.e. L admits a countable base which is free of supercompact elements), a monotone version of the Katětov-Tong insertion theorem for L-valued functions is established. We also provide a monotone lattice-valued version of Urysohn’s lemma. Both results yield new characterizations of monotonically normal spaces. Moreover, extension of lattice-valued functions under additional assumptions is shown to characterize also monotone normality.

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Abstract  

Let a1<a2<... be an infinite sequence of positive integers, let k≥2 be a fixed integer and denote by Rk(n) the number of solutions of n=ai1+ai2+...+aik. P. Erdős and A. Srkzy proved that if F(n) is a monotonic increasing arithmetic function with F(n)→+∞ and F(n)=o(n(log n)-2) then |R2(n)-F(n)| =o((F(n))1/2) cannot hold. The aim of this paper is to extend this result to k>2.

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Abstract  

In this paper an extension of a Hölder-type inequality given in [C. E. M. Pearce and J. Pečarić, On an extension of Hölder’s inequality, Bull. Austral. Math. Soc., 51(1995), 453–458] is improved using log-convexity. Furthermore, new Cauchy-type means are defined and their monotonicity property is proven.

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Abstract  

This study utilizes neural network to explore the nonlinear relationships between corporate performance and the patent traits measured from Herfindahl-Hirschman Index of patents (HHI of patents), patent citations, and relative patent position in the most important technological field (RPPMIT) in the US pharmaceutical industry. The results show that HHI of patents and RPPMIT have nonlinearly and monotonically positive influences upon corporate performance, while the influence of patent citations is nonlinearly U-shaped. Therefore, pharmaceutical companies should raise the degrees of the leading position in their most important technological fields and the centralization of their technological capabilities to enhance corporate performance.

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Abstract  

Let X ⊂ ℝ be an interval of positive length and define the set Δ = {(x, y) ∈ X × X | xy}. We give the solution of the equation

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$F(G_1 (x,y),G_2 (u,v)) = G(F(x,u),F(y,v)),$$ \end{document}
which holds for all (x, y) ∈ Δ and (u, υ) ∈ Δ, where the functions F: XX, G 1: Δ → X, G 2: Δ → X, and G: F(X, X) × F(X, X) → X are continuous and strictly monotonic in each variable.

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Abstract  

Let I ⊂ ℝ be an interval and κ, λ ∈ ℝ / {0, 1}, µ, ν ∈ (0, 1). We find all pairs (φ, ψ) of continuous and strictly monotonic functions mapping I into ℝ and satisfying the functional equation

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\kappa x + (1 - \kappa )y = \lambda \phi ^{ - 1} (\mu \phi (x) + (1 - \mu )\phi (y)) + (1 - \lambda )\psi ^{ - 1} (\nu \psi (x) + (1 - \nu )\psi (y))$$ \end{document}
which generalizes the Matkowski-Sutô equation. The paper completes a research stemming in the theory of invariant means.

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Brighi, L. and John, R., Characterizations of pseudomonotone maps and economic equilibrium, Journal of Statistics & Management Systems , Special Volume on Generalized Convexity, Generalized Monotonicity

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John, R. , Variational inequalities and pseudomonotone functions: some characterizations, Proceedings of the 5th Symposium on Generalized Convexity and Generalized Monotonicity , eds. J.-P. Crouzeix, J.-E. Martinez-Legaz and M. Volle, Luminy

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