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Vol.10 No.3
Abstract
Weak commutativity of a pair of maps was introduced by Sessa [On a weak commutativity condition of mappings in fixed point considerations. Publ. Inst. Math. (Beograd) (N.S.) 32(40) (1982),149-153] in fixed point considerations. Thereafter a number of generalizations of this notion has been obtained. The purpose of this paper is to present a brief development of weaker forms of commuting maps, and to obtain two fixed point theorems for noncommuting and noncontinuous maps on noncomplete metric spaces.
Abstract
In this paper we present a new and natural interpretation of subhypergroups in a partially ordered algebra. Then we study their connection with corresponding crisp concepts through their newly defined Q-cuts. The theorems proved also highly generalized the existing ones.
Abstract
The purpose of this paper is to Show the relationships between three forms of the axiom of choice and well-ordering in an elementary topos.
Abstract
In this paper, we initiate the study of some annihilator conditions on polynomials which were used by Kaplansky [Rings of operators. W. A. Benjamin, Inc., New York, 1968] to abstract the algebra of bounded linear operators on a Hilbert spaces with Baer condition. On the other hand, p.p.-rings were introduced by Hattori [A foundation of torsion theory for modules over general rings. Nagoya Math. J. 17 (1960) 147-158] to study the torsion theory. The purpose of this paper is to introduce the near-rings with Baer condition and near-rings with p.p. condition which are somewhat different from ring case, and to extend a results of Armendariz [A note on extensions of Baer and P.P.-rings. J. Austral. Math. Soc. 18 (1974), 470-473] and Jøndrup [p.p. rings and finitely generated flat ideals. Proc. Amer. Math. Soc. 28 (1971) 431-435].
Abstract
It is shown that every almost linear mapping <TEX>$h{\;}:{\;}X{\;}{\rightarrow}{\;}Y$</TEX> of a complex normed space X to a complex normed space Y is a linen. mapping when h(rx) = rh(x) (r > 0,<TEX>$r\;{\neq}\;1$</TEX) holds for all <TEX>$x{\;}{\in}{\;}X$</TEX>, that every almost quadratic mapping <TEX>$h{\;}:{\;}X{\;}{\rightarrow}{\;}Y$</TEX> of a complex normed space X to a complex normed space Y is a quadratic mapping when <TEX>$h(rx){\;}={\;}r^2h(x){\;}(r{\;}>{\;}0,r\;{\neq}\;1)$</TEX> holds for all <TEX>$x{\;}{\in}{\;}X$</TEX>, and that every almost cubic mapping <TEX>$h{\;}:{\;}X{\;}{\rightarrow}{\;}Y$</TEX> of a complex normed space X to a complex normed space Y is a cubic mapping when <TEX>$h(rx){\;}={\;}r^3h(x){\;}(r{\;}>{\;}0,r\;{\neq}\;1)$</TEX> holds for all <TEX>$x{\;}{\in}{\;}X$</TEX>.
Abstract
Let X and Y be n-dimensional Euclidean spaces with <TEX>$n\;{\geq}\;3$</TEX>. In this paper, we generalize a classical theorem of Bookman and Quarles by proving that if a mapping, from a half space of X into Y, preserves a distance <TEX>$\rho$</TEX>, then the restriction of f to a subset of the half space is an isometry.