Therefore, the standard monotonicity
The neutrosophic opening satisfies the monotonicity
[for all]A,B [member of] NC([Z.
In coalition formation theory, a comparison relation should satisfy the conditions of transitivity and monotonicity
A notable consequence, which will be explored in the next section, is that the regulated output may be incentive compatible even if standard monotonicity
Hence, the same monotonicity
applies to the optimal solution [L.
In this paper, we are concerned with the the relation between the positivity of the vth order nabla q-fractional difference and the monotonicity
and convexity of f (t).
Furthermore, when assuming exogeneity of X wrt Y in addition to monotonicity
, the expressions given in Eq.
In 2003, Fang and Huang  introduced a new concept of relaxed [eta]-[alpha] monotonicity
and obtained the existence of solution for variational-like inequalities in reflexive Banach spaces.
In [2, 3], the authors discussed the monotonicity
and logarithmic convexity properties of the one-parameter mean [J.
Teo, Generalized invexity and generalized invariant monotonicity
However, it suffers from the disadvantages first noticed by Sen (1976) in the unidimensional context, namely being insensitive to the depth and distribution of poverty, violating monotonicity
and the transfer axiom.
First, we assume strong monotonicity
of the social wealth function, which suppresses the need to explicitly treat prices in analysing wealth in Malthus's critique of Smith.
Markov  and Stieltjes  were the first who studied the monotonicity
of zeros of a parameter-dependent sequence of OPRL as functions of the involved parameter.
A risk measure is coherent if and only if it satisfies all four of these conditions: translation invariance, homogeneity, monotonicity
, and subadditivity [Artzner et al.
Here, the notions of adaptive monotonicity
and adaptive submodularity reduce to the classical notion of monotonicity
and submodularity for set functions, which have been extensively studied in economics, operations research, theoretical computer science and other fields.