With the proliferation of distributed generators and energy storage systems, traditional passive consumers in power systems have been gradually evolving into so-called “prosumers,” i.e., proactive consumers, which can both produce consume power. To encourage exchange among prosumers, sharing is increasingly adopted, usually formulated as a generalized Nash game (GNG). In this paper, approach pr...

Dragomir introduced the Jensen-type inequality for harmonic convex functions (HCF) and Baloch et al. studied its different variants, such as h -convex functions. In this paper, we aim to establish functional form of inequalities presented by prove superadditivity monotonicity properties these functionals. Furthermore, de...

In this article, we introduce a new notion of generalized convex fuzzy mapping known as strongly preinvex on the invex set. Firstly, have investigated some properties mapping. particular, establish equivalence among mapping, and monotonicity. We also prove that optimality conditions for sum G-differentiable mappings non-G-differentiable can be characterized by mixed variational-like inequalitie...

We analyze the problem of fully implementing a social choice set in ex post equilibrium. We identify an ex post monotonicity condition that is necessary and—in economic environments—sufficient for full implementation in ex post equilibrium. We also identify an ex post monotonicity no veto condition that is sufficient. Ex post monotonicity is satisfied in all single crossing environments with st...

The assumption of latent monotonicity in item response theory models for dichotomous data cannot be evaluated directly, but observable consequences such as manifest monotonicity facilitate the assessment of latent monotonicity in real data. Standard methods for evaluating manifest monotonicity typically produce a test statistic that is geared toward falsification, which can only provide indirec...