Abstract In a real Hilbert space, let the VIP, GSVI, HVI, and CFPP denote variational inequality problem, general system of inequalities, hierarchical inequality, common fixed-point problem countable family uniformly Lipschitzian pseudocontractive mappings an asymptotically nonexpansive mapping, respectively. We design two Mann implicit composite subgradient extragradient algorithms with line-s...

Let {Ti}i=1 be a finite family of nonexpansive self-maps of H . Denote the common fixed points set of {Ti}i=1 by ⋂N i=1 Fix(Ti). Let F : H → H be a mapping such that for some constants k,η > 0, F is k-Lipschitzian and η-strongly monotone. Let {αn}n=1 ⊂ (0,1), {λn}n=1 ⊂ [0,1) and take a fixed number μ ∈ (0,2η/k2). The iterative schemes concerning nonlinear operators have been studied extensively...

and Applied Analysis 3 to a fixed point of the mapping T , which is also a solution of VI 1.5 defined on the set of fixed points of T . As direct consequences, we obtain the unique minimum-norm fixed point of T . Namely, we find the unique solution of the quadratic minimization problem: ‖x̃‖ min{‖x‖ : x ∈ Fix T }. 2. Preliminaries and Lemmas Throughout this paper, when {xn} is a sequence inH, xn...

In this paper, we introduce a new iterative scheme for finding a common element of the fixed points set of a countable family of uniformly Lipschitzian generalized asymptotically quasi-nonexpansive mappings and the solutions set of equilibrium problems. Some strong convergence theorems of the proposed iterative scheme are established by using the concept of W -mappings of a countable family of ...

This paper deals with Lipschitzian t-norms. A partial answer to an open problem of Alsina, Frank and Schweizer is given with regard to strict t-norms with smooth additive generators. A new notion of local Lipschitzianity for arbitrary tnorms is introduced. Some remarkable examples of non-Lipschitzian continuous triangular norms are provided.

This paper concerns applications of advanced techniques of variational analysis and generalized differentiation to parametric problems of semi-infinite and infinite programming, where decision variables run over finite-dimensional and infinite-dimensional spaces, respectively. Part I is primarily devoted to the study of robust Lipschitzian stability of feasible solutions maps for such problems ...

A sequence (Mk) of closed subsets of Rn converges normally to M ⊂ Rn if (sc) M = lim supMk = lim inf Mk in the sense of Painlevé–Kuratowski and (nc) lim sup G(NMk ) ⊂ G(NM ), where G(NM ) (resp., G(NMk )) denotes the graph of NM (resp., NMk ), Clarke’s normal cone to M (resp., Mk). This paper studies the normal convergence of subsets of Rn and mainly shows two results. The first result states t...

Consider the linear space n of polynomials of degree n or less over the complex field. The abscissa mapping on n is the mapping that takes a polynomial to the maximum real part of its roots. This mapping plays a key role in the study of stability properties for linear systems. Burke and Overton have shown that the abscissa mapping is everywhere subdifferentially regular in the sense of Clarke o...

Lipschitzian and kernel aggregation operators with respect to the natural T indistinguishability operator ET and their powers are studied. A t-norm T is proved to be ET -lipschitzian, and is interpreted as a fuzzy point and a fuzzy map as well. Given an archimedean t-norm T with additive generator t, the quasi-arithmetic mean generated by t is proved to be the more stable aggregation operator w...