Compatible Pair Of Mappings Research Articles

On Pair of Compatible Mappings and Coincidence Point Theorems in b-Metric Spaces

The main goal of this study is to give two different results for a couple of compatible self-mappings. The first result provides the necessary condition for the existence of a coincidence point for a pair of mappings that are partially weakly increasing in partially ordered b-metric spaces. Additionally, we establish a fixed point result in order to guarantee the uniqueness of common fixed points for pair of maps satisfying the b-(E.A.) Property. Our findings extends and improve well established results of existing literature. In order highlight the distinctiveness of our main theorems, two discrete examples with Tabular and Graphical representations are also presented.

Fixed point theorems under weakly contractive conditions via auxiliary functions in ordered $G$-metric spaces

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 existence and uniqueness of solutions for a boundary value problem for certain second order ODE and the respective integral equation.

Weak Coupled Coincidence Point Results Having a Partially Ordering in Fuzzy Metric Spaces

Coupled coincidence and fixed point problems have been in the focus of the research interest for last few years. The problem was introduced in fuzzy metric spaces only very recently. In this paper, we work out a weak coupled coincidence point theorem for a compatible pair of mappings in fuzzy metric spaces. As one of the corollaries we have a weak coupled fuzzy contraction mapping theorem. The space is endowed with a partial ordering. We use a combination of analytic and order theoretic concepts in the proof of our main theorem. The result is illustrated with an example.

Points of coincidence for weakly compatible pair of mappings in cone metric spaces

In this paper, some new existence and uniqueness of points of coincidence of weakly compatible pair of mappings is obtained, which does not satisfy continuity and commutativity. The conditions are weaker than the usual conditions in cone metric spaces. Some common fixed point theorems are obtained, these results improve several well-known comparable results in literatures. For further, some examples are given to support our results.

Suzuki type common fixed point theorem in complete metric space and partial metric space

In this paper we establish that a pair of compatible mappings have unique common fixed point in metric and partial metric spaces respectively. The mappings are Suzuki type. We give examples to illustrate our results.

Some Generalizations of Jungck's Fixed Point Theorem

We are going to generalize the Jungck's fixed point theorem for commuting mappings by mean of the concepts of altering distance functions and compatible pair of mappings, as well as, by using contractive inequalities of integral type and contractive inequalities depending on another function.

Coupled coincidence point theorems in ordered metric spaces

In this paper we extend the coupled contraction mapping theorem proved in partially ordered metric spaces by Gnana Bhaskar and Lakshmikantham (Nonlinear Anal. TMA 65:1379–1393, 2006) to a coupled coincidence point result for a pair of compatible mappings. A control function has been used in our theorem. The mappings are assumed to satisfy a weak contractive inequality. Our theorem improves the results of Harjani et al. (Nonlinear Anal. TMA 74:1749–1760, 2011). The result we have established is illustrated with an example which also shows that the improvement is actual.

Boundary Value Problems with Compatible Boundary Conditions

If Y is a subset of the space ℝn × ℝn, we call a pair of continuous functions U, V Y-compatible, if they map the space ℝn into itself and satisfy Ux · Vy ≥ 0, for all (x, y) ∈ Y with x · y ≥ 0. (Dot denotes inner product.) In this paper a nonlinear two point boundary value problem for a second order ordinary differential n-dimensional system is investigated, provided the boundary conditions are given via a pair of compatible mappings. By using a truncation of the initial equation and restrictions of its domain, Brouwer's fixed point theorem is applied to the composition of the consequent mapping with some projections and a one-parameter family of fixed points P δ is obtained. Then passing to the limits as δ tends to zero the so-obtained accumulation points are solutions of the problem.