A Multiple Fixed Point Result for θ , ϕ , ψ -Type Contractions in the Partially Ordered s -Distance Spaces with an Application

In this manuscript, the aim is to prove a multiple fixed point (FP) result for partially ordered s -distance spaces under θ , ϕ , ψ -type weak contractive condition. The result will generalize some well-known results in literature such as coupled FP (Guo and Lakshmikantham, 1987), triple fixed point (Berinde and Borcut, 2011), and quadruple FP results (Karapinar, 2011). Moreover, to validate the result, an application for the existence of solution of a system of integral equations is also provided.

Examples of Pomonoids of Full Transformations of a Poset

In this research, the partially ordered monoid (simple pomonoid) full transformations of a poset O(X) is studied, and some related properties are examined. We show that when the poset X_ is not totally ordered, the pomonoid of all decreasing singular self-maps of a poset X_ (denoted by S^-) and the pomonoid of all increasing singular self-maps of a poset X_ (denoted by S^+) may not be generally isomorphic. Some specific partial ordered relations are considered, and the cardinalities of S^- and S^+ under these relations are found. The set of fixed, decreasing, and increasing points of mapping α in O(X) are also investigated. KEYWORDS Posets, pomonoids, full transformations

A Krasnoselskii–Ishikawa Iterative Algorithm for Monotone Reich Contractions in Partially Ordered Banach Spaces with an Application

Iterative algorithms have been utilized for the computation of approximate solutions of stationary and evolutionary problems associated with differential equations. The aim of this article is to introduce concepts of monotone Reich and Chatterjea nonexpansive mappings on partially ordered Banach spaces. We describe sufficient conditions for the existence of an approximate fixed-point sequence (AFPS) and prove certain fixed-point results using the Krasnoselskii–Ishikawa iterative algorithm. Moreover, we present some interesting examples to highlight the superiority of our results. Lastly, we provide both weak and strong convergence results for such mappings and consider an application of our results to prove the existence of a solution to an initial value problem.

Probability Distributions on Partially Ordered Sets and Network Interdiction Games

This article poses the following problem: Does there exist a probability distribution over subsets of a finite partially ordered set (poset), such that a set of constraints involving marginal probabilities of the poset’s elements and maximal chains is satisfied? We present a combinatorial algorithm to positively resolve this question. The algorithm can be implemented in polynomial time in the special case where maximal chain probabilities are affine functions of their elements. This existence problem is relevant for the equilibrium characterization of a generic strategic interdiction game on a capacitated flow network. The game involves a routing entity that sends its flow through the network while facing path transportation costs and an interdictor who simultaneously interdicts one or more edges while facing edge interdiction costs. Using our existence result on posets and strict complementary slackness in linear programming, we show that the Nash equilibria of this game can be fully described using primal and dual solutions of a minimum-cost circulation problem. Our analysis provides a new characterization of the critical components in the interdiction game. It also leads to a polynomial-time approach for equilibrium computation.

The Foundations of Branching Space-Times

In this chapter the reader is guided through the construction of the core theory of Branching Space-Times. This discursive approach culminates in proposing a set of postulates that a structure of the core theory of Branching Space-Times (common BST) has to satisfy. The theory’s basic notion is that of a set of events, partially ordered by a pre-causal relation. Histories are then defined as maximal directed subsets of the base set. The chapter proves essential facts about histories and the postulates that the core of BST is assumed to satisfy. Among other things, it proves the so-called M-property that determines how any two point event in a common BST structure are related.

Strong Stationary Duality and Algebraic Duality for Continuous Time Möbius Monotone Markov Chains

Under the assumption of Möbius monotonicity, we develop the theory of strong stationary duality for continuous time Markov chains on the finite partially ordered state space, we also construct a nonexplosive algebraic duality for continuous time Markov chains on Finally, we present an application to the two-dimensional birth and death chain.