In this paper, we establish the convergence properties for a majorized alternating direction method of multipliers for linearly constrained convex optimization problems,whose objectives contain coupled functions.Our convergence analysis relies on the generalized Mean-Value Theorem, which plays an important role to properly control the cross terms due to the presence of coupled objective functio...

Abstract When the ordering of variables is fixed, e.g., x1 ≥ x2 ≥ · · · ≥ xn, the monomial X α = x α1 1 · · ·xn n majorizing the monomial X β = x1 1 · · ·xn n (|α| = |β|) means that ∑k i=1 αi ≥ ∑k i=1 βi (k = 1, · · · , n − 1). In this paper, a necessary condition of positively terminating of a general successive difference substitution algorithm (KSDS) for an input f is obtained by using a maj...

In the early 70’s, D.M. Campbell published three papers on majorizationsubordination results for locally univalent functions. In particular, he showed that if F is linearly invariant of order α and if f is subordinate to F on {z : |z| < 1}, then f ′ is majorized by F ′ on {z : |z| < m(α)} where m(α) = α+ 1− √ α2 + 2α, provided α ≥ 1.65. He conjectured, in fact, that this result also held for 1....

This paper provides some useful results for convex risk measures. In fact, we consider convex functions on a locally convex vector space E which are monotone with respect to the preference relation implied by some convex cone and invariant with respect to some numeraire (“cash”). As a main result, for any function f , we find the greatest closed convex monotone and cash-invariant function major...

Abstract. In this paper, a complete solution of a problem involving generalized majorization of partitions is given: for two pairs of partitions (d, a) and (c,b) necessary and sufficient conditions for the existence of a partition g that is majorized by both pairs is determined. The obtained conditions are explicit, the solution is constructive and it uses novel techniques and indices. Although...

we prove a strong convergence result for a sequence generated by halpern's type iteration for approximating a common fixed point of a countable family of quasi-lipschitzian mappings in a real hilbert space. consequently, we apply our results to the problem of finding a common fixed point of asymptotically nonexpansive mappings, an equilibrium problem, and a variational inequality problem for co...

recently, zhang and song [q. zhang, y. song, fixed point theory forgeneralized $varphi$-weak contractions,appl. math. lett. 22(2009) 75-78] proved a common fixed point theorem for two mapssatisfying generalized $varphi$-weak contractions. in this paper, we prove a common fixed point theorem fora family of compatible maps. in fact, a new generalization of zhangand song's theorem is given.

binayak et al in [1] proved a fixed point of generalized kannan type-mappings in generalized menger spaces. in this paper we extend gen- eralized kannan-type mappings in generalized fuzzy metric spaces. then we prove a fixed point theorem of this kind of mapping in generalized fuzzy metric spaces. finally we present an example of our main result.

we introduce an implicit method for nding a common element of the set of solutions of systems of equilibrium problems and the set of common xed points of a sequence of nonexpansive mappings and a representation of nonexpansive mappings. then we prove the strong convergence of the proposed implicit schemes to the unique solution of a variational inequality, which is the optimality condition fo...

This article is concerned with a strong unique continuation property of forward differential inequality abstracted from parabolic equations proposed on convex domain $ \Omega prescribed some regularity and growth conditions. Our results show that the value solutions can be determined uniquely by its an arbitrary open subset \omega in at any given positive time T $. We also derive quantitative n...