A strongly convex function of simple structure (for example, separable) is minimized under affine constraints. A dual problem is constructed and solved by applying a fast gradient method. The necessary propertie
In this paper we use basic properties of strongly convex functions to obtain new inequalities including Jensen's type and Jensen-Mercer type inequalities. Applications for special means are pointed out as well. We also give a Jensen's operator inequality for strongly convex functions. As a corolla...
Ponnusamy and Singh =-=[4]-=- obtained bounds on λ such that the Alexander transform of f ∈ , satisfying f ′ ≺ 1+λz, is uniformly convex. We extend their result in two directions. Specifically, we find condition on λ such that t...Ponnusamy, S. and Singh, V., "Criteria ...
Then, an adversary chooses a convex loss function ft(x):X↦R, and incurs a loss ft(xt) to the player. The performance of the player is measured by the regret RT=∑t=1Tft(xt)−minx∈X∑t=1Tft(x), which is the gap between the cumulative loss of the player and an optimal ...
fixed nonsmooth functionThis paper presents an algorithmic solution, the adaptive projected subgradient method, to the problem of asymptotically minimizing a certain sequence of non-negative continuous convex functions over the fixed point set of a strongly attracting nonexpansive mapping in a real Hilbert...
F:[0,T]×K→L2([0,T],Rq), where K is a convex subset of R+q, is said to be: • hemicontinuous in the sense of Fan (briefly F-hemicontinuous) if and only if for all v∈L2([0,T],R+q) the function u→∫0T〈F(t,u(t)),u(t)-v(t)〉dtis lower semicontinuous on...
Theorem 1.5 For every f∈Hp,ψ(Y′), there is a function F∈Hp,ψ(U′) such that F=f on X′ . Remark 1.6 Let M⊂⊂N be a strongly pseudoconvex manifold. As before,we assume thatπ1(M)=π1(N) and N is strongly pseudoconvex, as well. Then there exist a normal Stein sp...
The purpose of this paper is to introduce the spaces of sequences that are strongly almost (ω, λ, q)-summable with respect to a modulus function. We give some relations related to these sequence spaces. It is also shown that if a sequence is strongly (
Some applications of discrete selectivity and Banakh property in function spaces 2020, European Journal of Mathematics Functional characterizations of countable tychonoff spaces 2019, Journal of Convex Analysis Closed discrete selections for sequences of open sets in function spaces 2018, Acta Mathematica Hu...
iffis a strongly convex function then its level sets{x:f(x)≤λ}are bounded for eachλandfhas a unique minimum on every closed convex set. Numerous properties and applications of them can be found in the literature (see, for instance, [9,13,14,17,19,20,26,29,35–37]). Recently,...