Necessary solvability conditions of systems of linear extremal equations

Solvability of Systems of Linear Operator Equations

Let G be a semigroup of commuting linear operators on a linear space S with the group operation of composition. The solvability of the system of equations /,/ = ,■, i = I, ... , r, where /, e G and j e S , was considered by Dahmen and Micchelli in their studies of the dimension of the kernel space of certain linear operators. The compatibility conditions Ijfr = Irfj , i ^ j , are necessar...

Solvability of Systems of Linear Interval Equations

Solvability of systems of interval linear equations and inequalities

This chapter deals with solvability and feasibility (i.e., nonnegative solvability) of systems of interval linear equations and inequalities. After a few preliminary sections, we delineate in Section 2.6 eight decision problems (weak solvability of equations through strong feasibility of inequalities) that are then solved in eight successive sections 2.7 to 2.14. It turns out that four problems...

Solvability of Parametric Interval Linear Systems of Equations and Inequalities

Considered are linear algebraic systems of equations and/or inequalities involving linear dependencies between interval-valued parameters. The goal is to characterize weak and strong solvability of such systems. Since any parametric interval equation is equivalent to a system of parametric interval inequalities, the focus is on the latter. We discuss an algorithmic procedure for characterizing ...

On the $c_{0}$-solvability of a class of infinite systems of functional-integral equations

  In this paper, an existence result for a class of infinite systems of functional-integral equations in the Banach sequence space $c_{0}$ is established via the well-known Schauder fixed-point theorem together with a criterion of compactness in the space $c_{0}$. Furthermore, we include some remarks to show the vastity of the class of infinite systems which can be covered by our result. The a...