Measurability of (M, N)-Wright convex functions

Convexity properties of functions defined on metric Abelian groups

“…Then there exist x, y ∈ D such that z ∈ {x, y} and T (x) + (I − T )(y) ∈ D n−1 . Then f (T (x) + (I − T )(y)) > −∞ and, by the (T, t)-convexity of f , (14) holds. The left hand side being finite, the condition t(1−t) > 0 implies that f (x) as well as f (y) are also finite, which yields that f is finite at z.…”

“…The structure and properties of t-convex sets and t-quasiconvex, t-Wright convex, and t-convex functions and their generalizations have been investigated in a large number of recent papers, see e.g. [1,6,7,9,10,[12][13][14][15][16][17][18][19][20][21][22][23]25,[27][28][29][30][31][32][33][34][35]39].…”

“…Furthermore, it turned out that for some second degree algebraic numbers the answer is positive whereas for some second degree algebraic numbers it is negative. Bernstein-Doetsch-type theorems for Wright convex functions were established by Olbryś [29] and by Lewicki [14,15]. On the other hand, in [6] Bernstein-Doetsch-type theorems were proven for quasiconvex functions.…”

Comparing Realistic Subthalamic Nucleus Neuron Models

“…Spike detection was done by thresholding of simulated extracellular [23] potential. We determined the threshold voltage as the average of the maximum peak value and the minimum peak value of action potentials.…”

A majorization inequality for Wright-convex functions revisited

“…In the theory of generalized convex functions, Wright-convexity is an important notion, studied and used in many papers, since its introduction in Wright [14], 1954 (see, e.g., Kominek [1], Lewicki [2], Maksa and Páles [3], Ming-In Ho [6], Mrowiec [7], Ng [8], Pecarić et al [10], Tseng et al [13]). …”