As with many mathematical concepts these axioms are chosen to ensure that two things are equal if and only if some property expressible in terms of the concept holds. For a metric space, x = y if and only if d(x, y) = 0. Thus as there is the equality relation x = y in a metric space, so there is what we call an indistancy relation d(x, y) = 0. Axioms M1 and M2 work together to identify equality...

There are a lot of fixed and common fixed point results in different types of spaces. For example, metric spaces, fuzzy metric spaces, and uniform spaces. One of the most interesting is partial metric space, which is defined by Matthews 1 . In partial metric spaces, the distance of a point in the self may not be zero. After the definition of partial metric space, Matthews proved the partial met...

We present some fixed point results for a single mapping and a pair of compatible mappings via auxiliary functions which satisfy a generalized weakly contractive condition in partially ordered complete $G$-metric spaces. Some examples are furnished to illustrate the useability of our main results. At the end, an application is presented to the study of exi...

In this paper, we prove some fixed point theorems for ordered Reich type contraction in cone rectangular metric spaces without assuming the normality of cone. Our results generalize and extend some recent results in cone rectangular metric spaces, cone metric spaces and rectangular metric space. Some examples illustrating the results are included.