Given a weakly convergent sequence of positive functions in W 1,p 0 (Ω), we prove the equivalence between its convergence in the sense of obstacles and the lower semicontinuity of the term by term duality product associated to (the p-Laplacian of) weakly convergent sequences of p-superharmonic functions of W 1,p 0 (Ω). This result implicitly gives new characterizations for both the convergence ...

We study conjugate and Lagrange dualities for composite optimization problems within the framework of abstract convexity. provide conditions zero duality gap in duality. For duality, intersection property is applied to obtain gap. Connection between dual also established. Examples related convex weakly functions are given.

A new notion of higher-order weakly generalized adjacent epiderivative for a set-valued map is introduced. By virtue of the epiderivative and weak minimality, a higher-order Mond-Weir type dual problem and a higher-order Wolfe type dual problem are introduced for a constrained setvalued optimization problem, respectively. Then, corresponding weak duality, strong duality and converse duality the...

For the Fr'{e}chet algebras $(A, (p_k))$ and $(B, (q_k))$ and $n in mathbb{N}$, $ngeq 2$, a linear map $T:A rightarrow B$ is called textit{almost $n$-multiplicative}, with respect to $(p_k)$ and $(q_k)$, if there exists $varepsilongeq 0$ such that$$q_k(Ta_1a_2cdots a_n-Ta_1Ta_2cdots Ta_n)leq varepsilon p_k(a_1) p_k(a_2)cdots p_k(a_n),$$for each $kin mathbb{N}$ and $a_1, a_2, ldots, a_nin A$. Th...

we consider the space of weakly almost periodic functions on a transformation semigroup (s, x , ?) and show that if x is a locally compact noncompact uniform space, and ? is a separately continuous, separately proper, and equicontinuous action of s on x, then every continuous function on x, vanishing at infinity is weakly almost periodic. we also use a number of diverse examples to show that th...

Several combinatorial structures exhibit a duality relation that yields interesting theorems, and, sometimes, useful explanations or interpretations of results that do not concern duality explicitly. We present a common characterization of the duality relations associated with matroids, clutters (Sperner families), oriented matroids, and weakly oriented matroids. The same conditions characteriz...

We consider the discrete-time voter model on complete bipartite graphs and study quasi-stationary distribution (QSD) for as size of one partitions tends to infinity while other partition remains fixed. show that QSDs converge weakly a nontrivial limit which features consensus with exception random number dissenting vertices in large partition. Moreover, we explicitly calculate law dissenters it...

The purpose of this article is to introduce two iterative algorithms for finding a common fixed point of a semigroup of asymptotically nonexpansive mappings which is a unique solution of some variational inequality. We provide two algorithms, one implicit and another explicit, from which strong convergence theorems are obtained in a uniformly convex Banach space, which admits a weakly continuou...