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We introduce a notion of quasi regularity for points with respect to the inclusion F (x) ∈ C, where F is a nonlinear Fréchet differentiable function from Rv to Rm. When C is the set of minimum points of a convex real-valued function h on Rm and F ′ satisfies the L-average Lipschitz condition of Wang, we use the majorizing function technique to establish the(More)
For a general infinite system of convex inequalities in a Banach space, we study the basic constraint qualification and its relationship with other fundamental concepts, including various versions of conditions of Slater type, the Mangasarian–Fromovitz constraint qualification, as well as the Pshenichnyi–Levin–Valadier property introduced by Li, Nahak, and(More)
Diabetic nephropathy is an increasingly important cause of morbidity and mortality worldwide. A large body of evidence suggests that dyslipidemia has an important role in the progression of kidney disease in patients with diabetes. Lipids may induce renal injury by stimulating TGF-β, thereby inducing the production of reactive oxygen species and causing(More)
For an inequality system defined by an infinite family of proper convex functions, we introduce some new notions of constraint qualifications in terms of the epigraphs of the conjugates of these functions and study relationships between these new constraint qualifications and other wellknown constraint qualifications including the basic constraint(More)
Several fundamental concepts such as the basic constraint qualification (BCQ), the strong conical hull intersection property (CHIP), and the perturbations for convex systems of inequalities in Banach spaces (over R or C) are extended and studied; here the systems are not necessarily finite. Their relationships with each other in connection with the best(More)
Dynamic Contrast Enhanced (DCE) MRI is increasingly being used to assess changes in capillary permeability. Most quantitative techniques used to measure capillary permeability are based on the Fick equation that requires measurement of signal reflecting both plasma and tissue concentrations of the solute being tested. To date, most Magnetic Resonance(More)
To provide a Kolmogorov-type condition for characterizing a best approximation in a continuous complex-valued function space, it is usually assumed that the family of closed convex sets in the complex plane used to restrict the range satisfies a strong interior-point condition, and this excludes the interesting case when some t is a line-segment or a(More)
For an inequality system defined by a possibly infinite family of proper functions (not necessarily lower semicontinuous), we introduce some new notions of constraint qualifications in terms of the epigraphs of the conjugates of these functions. Under the new constraint qualifications, we obtain characterizations of those reverse-convex inequalities which(More)