We give an axiom C.C in symmetric spaces and investigate the relationships between C.C and axioms W3 , W4 , and H.E . We give some results on coinsidence and fixed-point theorems in symmetric spaces, and also, we give some examples for the results of Imdad et al. 2006 .
Abstract. Sign-solvable linear systems were introduced in modelling economic and physical systems where only qualitative information is known. Often economic and physical constraints require the entries of a solution to be nonnegative. Yet, to date the assumption of nonnegativity has been omitted in the study of sign-solvable linear systems. In this paper, the notions of signconsistency and sign-solvability of a constrained linear system Ax = b; x 0 0, are introduced. These notions give rise to new classes of sign patterns. The structure and the complexity of the recognition problem for each of these classes are studied. A qualitative analog of Farkas' Lemma is proven, and it is used to establish necessary and su cient conditionsfor the constrainedlinear system Ax = b; x 0 0 to be sign-consistent. Also, necessary and su cient conditions for the constrained linear system Ax = b; x 0 0 to be sign-solvable are determined, and these are used to establish a polynomialtime recognition algorithm. It is worth noting that the recognition problem for unconstrained sign-solvable linear systems is known to be NP-complete.
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