On some fixed points theorems in generalized complete metric spaces

On a Theorem of Khan in a Generalized Metric Space

“…For instance, see quasi metric spaces [1], generalized quasi metric spaces [2], pseudometric spaces ( [3], Chapter 2), approach spaces [4], -spaces [5], inframetric spaces [6], and -metric spaces [7]. Sometimes, as in [8,9], even the very notion of generalized metric spaces (or even gms [10]) is used, but it has a different meaning. In 2000, Branciari [11] introduced the notion of generalized metric space where the triangle inequality of a metric space is replaced by a rectangular inequality involving four terms instead of three.…”

Generalized uniform spaces, uniformly locally contractive set-valued dynamic systems and fıxed points

“…follows directly from (9), (10), (18), and (19). If i = 2, then we also note that, by (18), (9) and 11,…”

“…Recall that the investigations of fixed points of maps in complete generalized metric spaces appeared for the first time in Diaz and Margolis [8] and Margolis [9].…”

“…Our purpose in this article is to answer our question in the affirmative and providing the illustrating examples. More precisely, inspired by ideas of Diaz and Margolis [8], Margolis [9], Luxemburg [6], Jung [7], Nadler [[4], Th. 5], Covitz and Nadler [5] and Suzuki [10] and the above comments and observations, the concepts of the families…”

On generalized complete metric spaces

“…Some fixed point theorems of the alternative for contractions on such spaces had been proved which include, as a special case, the fixed point theorem of Banach for contractions on complete metric spaces (see [l]). For further information and references» see references [2] and [4].…”