Positivity最新文献

This paper investigates second-order optimality conditions for general constrained set-valued optimization problems in normed vector spaces under the set criterion. To this aim we introduce several new concepts of second-order directional derivatives for set-valued maps by means of excess from a set to another one, and discuss some of their properties. By virtue of these directional derivatives and by adopting the notion of set criterion intoduced by Kuroiwa, we obtain second-order necessary and sufficient optimality conditions in the primal form. Moreover, under some additional assumptions we obtain dual second-order necessary optimality conditions in terms of Lagrange–Fritz–John and in terms of Lagrange–Karush–Kuhn–Tucker multipliers.

We prove new singular value inequalities involving submultiplicative and subadditive functions of matrices. Singular value inequalities for sums and direct sums of matrices are also given.

Trust and reputation systems play a pivotal role in modern decentralized environments, fostering cooperation and mitigating risks in various online interactions. This paper introduces a variational formulation approach to model and analyze trust and reputation systems. By formulating trust and reputation as variational problems, this approach offers a novel perspective on understanding the underlying mechanisms governing trust establishment. The variational formulation provides a mathematical framework to determine the equilibrium weighted trust values, taking into account that each trustee tries to maximize its gain, namely the benefit minus the costs. The paper illustrates the applicability of this variational formulation through a pletora of simulations, demonstrating its effectiveness in modeling trust and reputation systems. Insights gained from this approach offer valuable guidance for the design and implementation of more reliable and efficient trust and reputation mechanisms in decentralized environments

In this work, an inexact proximal point algorithm is proposed for solving unconstrained multiobjective optimization problems with locally Lipschitz and quasi-convex objective functions. In this algorithm, we use quasi-distance in the regularization term and consider the (varepsilon )-approximate solution of the scalarization subproblem as well as the (varepsilon )-subdifferential in the optimality condition of the subproblem. This algorithm is shown to be well-defined. Then, it is proved that each accumulation point, if any, of the sequence generated by the algorithm is a Pareto-Clarke critical point of the problem.

We give a complete description of self-majorizing elements of a Banach lattice unital f-algebra. The idea comes from Luxemburg (Some Aspects of the Theory of Riesz Spaces, University of Arkansas Lecture Notes in Mathematics, 4, Fayetteville, Arkansas, (1979)).

In this paper, we introduce inductive limits of the Fréchet spaces (ell (p+)), (text {ces}(p+)), and (d(p+)) ((1 le p < infty )) and projective limits of the (LB)-spaces (ell (p-)), (text {ces}(p-)), and (d(p-)) ((1 < p le infty )). After having established some topological properties of such spaces as acyclicity and ultrabornologicity, we prove that the generalized Cesàro operators (C_t) ((0 le t le 1)) act continuously in these sequence spaces, and we determine the spectra. Finally, we study the ergodic properties, that is, power boundedness, (uniform) mean ergodicity, and supercyclicity, of the operators (C_t) acting in the (LF)-spaces and in the (PLB)-spaces mentioned above.

In this note we provide a new way to capture operators involving Laguerre polynomials by composition of an integral operator and a discrete operator. The new operator so obtained is a discrete operator. We give three examples by considering composition of Szász-Durrmeyer operator, exponential-type operator related to (2x^{3/2}) and the Phillips operator, respectively, with Szász-Mirakyan operators. In all cases we obtain positive linear, discretely defined operators which are based on Laguerre polynomials and approximate functions on the positive real half-axis.

In this paper, we introduce the concept of approximate Benson properly efficient solutions for the set-valued equilibrium problems (in short, SVEP) and investigate its properties. Under some suitable assumptions, the linear scalarization theorems for SVEP are obtained. Two nonlinear scalarization theorems for SVEP are presented. Based on the linear scalarization results, the nonemptiness and connectedness of the approximate Benson properly efficient solution set are established under some suitable conditions in real locally convex spaces. Some examples are also given to illustrate our results. The main results of this paper improve and generalize some known results in the literature.

The span of positive linear operators belonging to an operator linear class P and acting between Banach lattices is rarely a Banach space under the operator norm. We investigate the enveloping norm (Vert SVert _{text {r-P}}=inf {Vert TVert : pm Sle Tin text {P}}) on ({text {span}}(text {P}_+(E,F))) that is complete under rather mild assumptions on P.