In this paper, we first introduce the notion of $c$-affine functions for $c> 0$. Then we deal with some properties of strongly convex functions in real inner product spaces by using a quadratic support function at each point which is $c$-affine. Moreover, a Hyers–-Ulam stability result for strongly convex functions is shown.

in this paper, we first introduce the notion of $c$-affine functions for $c> 0$.then we deal with some properties of strongly convex functions in real inner product spaces by using a quadratic support function at each point which is $c$-affine. moreover, a hyers–-ulam stability result for strongly convex functions is shown.

‎Many optimization problems can be reduced to a problem with an increasing and co-radiant objective function by a suitable transformation of variables. Functions, which are increasing and co-radiant, have found many applications in microeconomic analysis. In this paper, the abstract convexity of positive valued affine increasing and co-radiant (ICR) functions are discussed. Moreover, the ...

This paper suggests a decentralized adaptive sliding mode formation procedure for affine nonlinear multi-quadrotor under a fixed directed topology wherever the followers are conquered by dynamical uncertainties. Compared with the previous studies which primarily concentrated on linear single-input single-output (SISO) agents or nonlinear agents with constant control gain, the proposed method is...

Abstract. In this paper, we define the notion of C*-affine maps in the unital *-rings and we investigate the C*-extreme points of the graph and epigraph of such maps. We show that for a C*-convex map f on a unital *-ring R satisfying the positive square root axiom with an additional condition, the graph of f is a C*-face of the epigraph of f. Moreover, we prove som...

Let G be a compact affine definable C group and let r be∞ or ω. We prove that the representative definable C functions on G is dense in the space of continuous functions on G. Moreover we compare the category of compact affine definable C groups D with that of compact real algebraic groups A.

The Boolean expression of an analogical proportion, i.e., a statement of the form “a is to b as c is to d”, expresses that “a differs from b as c differs from d, and vice-versa. This is the basis of an analogical inference principle, which is shown to be a particular instance of the analogical “jump”: from P (s), P (t), and Q(s), deduceQ(t). Roughly speaking, an analogical proportion sounds lik...

We give a type free formula for the expansion of k-Schur functions indexed by fundamental coweights within the affine nilCoxeter algebra. Explicit combinatorics are developed in affine type C.