Recently, Cho et al. [Y. J. Cho, R. Saadati, S. H. Wang, Common fixed point theorems on generalized distance in ordered cone metric spaces, Comput. Math. Appl. 61 (2011) 1254-1260] defined the concept of the c-distance in a cone metric space and proved some fixed point theorems on c-distance. In this paper, we prove some new fixed point and common fixed point theorems by using the distance in ordered cone metric spaces.

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.

A new and attractive metric space is a P-metric space which is a generalization of the concept of b-metric spaces. The generalization of the principle of Banach contraction has been carried out by many authors. Generalizations focus on the extension of metric spaces and the extension of contraction conditions. A few metrics, such as partial metrics, G-metrics, 2-metrics and Branciari metrics are some examples of metrics provided in this field. The aim of this paper is to present some common fixed point results for two mappings (one of them is weakly isotone increasing with respect to another) in the framework of ordered $p$-metric spaces. Our results are generalizations of the presented results in [H. K. Nashine, B. Samet and C. Vetro, Math. Comput. Modelling, 54 (2011) 712– 720] and [ J. R. Roshana, V. Parvaneh and Z. Kadelburg, J. Nonlinear Sci. Appl., 7 (2014), 229--245]. An example is also provided to support our results.

In this paper, recalling the structure of modified $G$-metric spaces(as a generalization of both $G$-metric and $G_b$-metric spaces), we present the notions of $\widetilde{G}$-rational contractive mappings and investigate the existence of fixedpoint for such mappings. We also provide examples and anapplication to illustrate the results presented herein.