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Inequality, welfare and monotonicity [PDF]

, 1997
We stablish a general relationship between the standard form of the individualistic social-welfare function and the "reduced-form" version that is expressed in terms of inequality and mean income. This shows the relationship between the property of monotonicity and the slope of the equity-efficient trade-off.
Yoram Amiel, Frank A Cowell
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Weighted Inequalities for Monotone Functions

Mathematische Nachrichten, 1995
AbstractWeighted norm inequalities are investigated by giving an extension of the Riesz convexity theorem to semi‐linear operators on monotone functions. Several properties of the classes B(p, n) and C(p, n) introduced by Neugebauer in [13] are given. In particular, we characterize the weight pairs w, v for which \documentclass{article}\pagestyle{empty}
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A continuation method for monotone variational inequalities

Mathematical Programming, 1995
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Bintong Chen, Patrick T. Harker
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Inequalities for some Monotone Matrix Functions

Canadian Journal of Mathematics, 1969
Let V denote a unitary vector space with inner product (x, y). A self-adjoint linear map T: V → V is positive (positive definite) if (Tx, x) ≧ 0 ((Tx, x) ≧ 0) for all x ≠ 0 in V. We write S ≧ T(S > T) if S and T are self-adjoint and S – T ≧ 0 (S – T > 0).
Marcus, M., Nikolai, P. J.
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Stable monotone variational inequalities

Mathematical Programming, 1990
The paper deals with variational inequalities associated with monotone multivalued operators and convex sets in reflexive Banach spaces. Many characterizations of stability, i.e. nonempty solution set in some neighborhood of the origin, are given. Most of the results are stated under the assumption that the operator is maximal monotone.
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Variational Inequalities with Generalized Monotone Operators

Mathematics of Operations Research, 1994
We investigate the variational inequality with pseudomonotone operators (in the sense of Karamardian) in Banach spaces. New existence results which extend many known results in infinite-dimensional spaces are derived under rather weak assumptions. New uniqueness results which also seem to be new even in finite-dimensional spaces are also derived.
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Monotonicity and Inequalities for the Generalized Distortion Function

Acta Mathematica Scientia, 2013
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Ma, Xiaoyan, Chu, Yuming, Wang, Fei
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Jensen’s inequality for operator monotone functions

Rendiconti del Circolo Matematico di Palermo, 1994
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Mond, B., Pečarić, J. E.
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On Monotone and Strongly Monotone Vector Variational Inequalities

2000
By constructing an example we show that the solution sets of a strongly monotone vector variational inequality and of its relaxed inequality can be different from each other. A sufficient condition for the coincidence of these solution sets is given for general vector variational inequalities; connectedness and path-connectedness of the solution sets ...
Nguyen Dong Yen, Gue Myung Lee
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Some Norm Inequalities for Completely Monotone Functions

SIAM Journal on Matrix Analysis and Applications, 2000
Summary: Let \(A\), \(B\) be \(n\times n\) complex positive semidefinite matrices, and let \(f\) be a completely monotone function on \([0,\infty)\). We prove that \(2|||f(A+ B)|||\leq |||f(2A)+ f(2B)|||\) for all unitarily invariant norms \(|||\cdot |||\).
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