Positivity最新文献

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.

This paper investigates nonsmooth multiobjective fractional programming (NMFP) with inequalities and equalities constraints in real reflexive Banach spaces. It derives a quotient calculus rule for computing the first- and second-order Clarke derivatives of fractional functions involving locally Lipschitz functions. A novel second-order Abadie-type regularity condition is presented, defined with the help of the Clarke directional derivative and the Páles–Zeidan second-order directional derivative. We establish both first- and second-order strong necessary optimality conditions, which contain some new information on multipliers and imply the strong KKT necessary conditions, for a Borwein-type properly efficient solution of NMFP by utilizing generalized directional derivatives. Moreover, it derives second-order sufficient optimality conditions for NMFP under a second-order generalized convexity assumption. Additionally, we derive duality results between NMFP and its second-order dual problem under some appropriate conditions

We show that for an ideal H in an Archimedean vector lattice F the following conditions are equivalent:

• H is a projection band;

• Any collection of mutually disjoint vectors in H, which is order bounded in F, is order bounded in H;

• H is an infinite meet-distributive element of the lattice ({mathcal {I}}_{F}) of all ideals in F in the sense that (bigcap nolimits _{Jin {mathcal {J}}}left( H+ Jright) =H+ bigcap {mathcal {J}}), for any ({mathcal {J}}subset {mathcal {I}}_{F}).

Additionally, we show that if F is uniformly complete and H is a uniformly closed principal ideal, then H is a projection band. In the process we investigate some order properties of lattices of continuous functions on Tychonoff topological spaces.

This paper proposes a line search technique to solve a special class of multi-objective optimization problems in which the objective functions are supposed to be convex but need not be differentiable. This is an iterative process to determine Pareto critical points. A suitable sub-problem is proposed at every iteration of the iterative process to determine the direction vector using the sub-differential of every objective function at that point. The proposed method is verified in numerical examples. This methodology does not bear any burden of selecting suitable parameters like the scalarization methods.