The purpose of this paper is to establish some fixed point results for a class generalized $(\phi, \psi)$-weak contraction mapping in partially ordered $b$-metric space. This necessarily have unique under relation Also, the common and coincidence points self mappings are presented. These generalize extend an existing literature. Some illustrations given at end support results.

Huang and Zhang 1 generalized the notion of metric space by replacing the set of real numbers by ordered Banach space, deffined a cone metric space, and established some fixed point theorems for contractive type mappings in a normal cone metric space. Subsequently, several other authors 2–5 studied the existence of common fixed point of mappings satisfying a contractive type condition in normal...

We study the topology of metric spaces which are definable in o-minimal expansions of ordered fields. We show that a definable metric space either contains an infinite definable discrete set or is definably homeomorphic to a definable set equipped with its euclidean topology. This implies that a separable metric space which is definable in an o-minimal expansion of the real field is definably h...

In this paper, the poset $BX$ of formal balls is studied in fuzzy partial metric space $(X,p,*)$. We introduce the notion of layered complete fuzzy partial metric space and get that the poset $BX$ of formal balls is a dcpo if and only if $(X,p,*)$ is layered complete fuzzy partial metric space.

In the present paper, we show the existence of a coupled fixed point for a non-decreasing mapping in partially ordered complete metric space using a partial order induced by an appropriate function φ. We also define the concept of weakly related mappings on an ordered space. Moreover common coupled fixed points for two and three weakly related mappings are also proved in the same space.

Let X denote a complete separable metric space, and let C(X) denote the linear space of all bounded continuous real-valued functions on X. The Lie generator of a strongly continuous semigroup T of continuous transformations in X is the linear operator in C(X) consisting of all ordered pairs (f; g) such that f; g 2 C(X), and for each x 2 X, g(x) is the derivative at 0 of f(T()x). We completely c...

Here, a new certain class of contractive mappings in the b-metric spaces is introduced. Some fixed point theorems are proved which generalize and modify the recent results in the literature. As an application, some results in the b-metric spaces endowed with a partial ordered are proved.