In this paper, we prove some unique fixed point theorems for a fuzzy mapping T satisfying certain rational contraction condition in a partially ordered metric space. Our results generalize some existing result.

In this paper, we prove several coupled common fixed point theorems for nonlinear mappings in a partially ordered probabilistic metric space. An example is presented to illustrate the main result of this paper.

In this paper we prove coupled fixed point theorem for mapping having the mixed monotone property in partially ordered metric space. We give an example to support of our result.

Let (X,1) be a partially ordered set and d be a metric on X such that (X, d) is a complete metric space. Let F : X ×X Ã X be a mixed monotone set valued mapping. We obtain sufficient conditions for the existence of a coupled fixed point of F.

*Correspondence: [email protected] 1Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia Full list of author information is available at the end of the article Abstract We first introduce the concept of b-metric-like space which generalizes the notions of partial metric space, metric-like space and b-metric space. Then we establish the existence and...

In this paper the authors prove existence, uniqueness and approximation of the solutions for initial value problems of nonlinear fractional differential equations with nonlocal conditions, using the operator theoretic technique in a partially ordered metric space. The main results rely on the Dhage iteration principle embodied in the recent hybrid fixed point theorem of Dhage (2014) in a partia...

We investigate the existence of well-ordered sequences of Baire 1 functions on separable metric spaces. Any set F of real valued functions defined on an arbitrary set X is partially ordered by the pointwise order, that is f ≤ g iff f(x) ≤ g(x) for all x ∈ X. In other words put f < g iff f(x) ≤ g(x) for all x ∈ X and f(x) 6= g(x) for at least one x ∈ X. Our aim will be to investigate the possibl...

We unify the concepts of G-metric, metric-like, and b-metric to define new notion of generalized b-metric-like space and discuss its topological and structural properties. In addition, certain fixed point theorems for two classes of G-α -admissible contractive mappings in such spaces are obtained and some new fixed point results are derived in corresponding partially ordered space. Moreover, so...