In this work, we present and study new ordered separation axioms, namely supra Tci-ordered spaces (briey, STci-ordered spaces), for i = 0,12, 1,112, 2. We illustrate the relationships among these ordered spaces with the help of examplesand we point out under what conditions the initiated ordered separationaxioms are hereditary properties. Also, we derive some results which connect someof STci-ordered spaces with some topological notions such as supra limit points andsupra disconnected spaces, and with some algebra notions such as largest and smallestelements. Furthermore, we investigate the image of theses ordered spaces underS?-homeomorphism maps. Finally, we verify that the nite ordered product of STci-ordered spaces is STci-ordered, for i = 0,12, 1,112.

Based on a complete Heyting algebra, we modify the definition of lattice-valued fuzzifying convergence space using fuzzy inclusion order and construct in this way a Cartesian-closed category, called the category of L-ordered fuzzifying convergence spaces, in which the category of L-fuzzifying topological spaces can be embedded. In addition, two new categories are introduced, which are called the category of principal L-ordered fuzzifying convergence spaces and that of topological L-ordered fuzzifying convergence spaces, and it is shown that they are isomorphic to the category of L-fuzzifying neighborhood spaces and that of L-fuzzifying topological spaces respectively.

In this paper, it is shown that the category of L-ordered fuzzifying convergence spaces contains the category of pretopological L-ordered fuzzifying convergence spaces as a bireflective subcategory and the latter contains the category of topological L-ordered fuzzifying convergence spaces as a bireflective subcategory. Also, it is proved that the category of L-ordered fuzzifying convergence spaces can be embedded in the category of stratified L-ordered convergence spaces as a coreflective subcategory.

In this paper, a concept of generalized weakly contraction map-pings in partially ordered fuzzy metric spaces is introduced and coincidence point theorems on partially ordered fuzzy metric spaces are proved. Also, as the corollary of these theorems, some common fixed point theorems on partially ordered fuzzy metric spaces are presented.

In this paper, we extend very recent fixed point theorems in the setting of ordered non-Archimedean fuzzy metric spaces. We present some fixed point theorems for self-mappings satisfying generalized $(\phi,\psi)$-contraction conditions in partially ordered complete non-Archimedean fuzzy metric spaces. On the other hand, we consider a more general class of auxiliary functions in the contractivity condition and we extend recently fixed point theorems for complete ordered non-Archimedean fuzzy metric spaces.  Also, we present a few examples to illustrate the validity of the results obtained in the paper.

In this paper, tripled coincidence points of mappings satisfying y-contractive conditions in the framework of partially ordered Gb -metric spaces are obtained. Our results extend the results of Aydiet al. [H. Aydi, E. Karapinar and W. Shatanawi, Tripled fixed point results in generalized metric space, J. Applied Math., Volume 2012, Article ID 314279, 10 pages]. Moreover, some examples of the main result are given.