标题：On convergent sequences and fixed point theorems in <mml:math alttext="$D$" id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>D</mml:mi></mml:math>-metric spaces
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2005
卷号：2005
DOI：10.1155/IJMMS.2005.1969
出版社：Hindawi Publishing Corporation
摘要：Examples of complete D-metric spaces are given in which every convergent
sequence has at most two limits and in which there are convergent
sequences with exactly two limits. Also an example of a complete
D-metric space having a convergent sequence with infinitely many
limits is given and, using the example, several fixed point
theorems in D-metric spaces are shown to be false. Modifications
of some of these theorems and their generalizations are obtained
either by imposing restrictions on the number of limits of certain
convergent sequences in the space or by assuming the sequential
continuity of the D-metric in any two variables and the theorems
so obtained are illustrated by means of examples.
