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This paper introduces compatible, non-compatible and weakly compatible maps on modified intuitionistic fuzzy soft metric spaces. Moreover, we have also extended fixed point theorems for two, four and six self maps that are weakly compatible in the setting of MIFSMS.

In this paper, we introduce a new class of contractive mapping in intuitionistic fuzzy metric space (IFMS). We establish fixed point theorems under such contractive mapping in complete IFMS and prove a common fixed point theorem for weakly compatible mappings under ϕ-contractive conditions in IFMS.

In this paper, we prove some common fixed point results of Ciric-type $$F_M$$ -contraction for weakly compatible mappings in metric space. We generalize common fixed point theorems for twelve self-mappings with (CLR)-property or common property (E.A). Also, we present examples and applications of these mappings in metric space and integral equations.

In this paper, we present some weakly compatible and quasi-contraction results for self-mappings in fuzzy cone metric spaces and prove some coincidence point and common fixed point theorems in the said space. Moreover, we use two Urysohn type integral equations to get the existence theorem for common solution to support our results. The two Urysohn type integral equations are as follows: $$\begin{aligned} &x(l)= \int _{0}^{1}K_{1}\bigl(l,v,x(v) \bigr)\,dv+g(l), \\ &y(l)= \int _{0}^{1}K_{2}\bigl(l,v,y(v) \bigr)\,dv+g(l), \end{aligned}$$ x(l)=∫01K1(l,v,x(v))dv+g(l),y(l)=∫01K2(l,v,y(v))dv+g(l), where $l\in [0,1]$l∈[0,1] and $x,y,g\in \mathbf{E}$x,y,g∈E, where E is a real Banach space and $K_{1},K_{2}:[0,1]\times [0,1]\times \mathbb{R}\to \mathbb{R}$K1,K2:[0,1]×[0,1]×R→R.

The aim of this manuscript is to discuss the existence and uniqueness of common solution for the following system of Urysohn integral equations: $$\begin{aligned} z(t)=\phi _{i}(t)+\int _{a}^{b}K_{i}(t,s,z(s)) ds, \end{aligned}$$ (0.1) where \(i=1,2,3,4\), \(a,b\in \mathbb {R}\) with \(a\le b\), \(t\in [a,b]\), \(z, \phi _{i} \in C([a,b],\mathbb {R}^n)\) and \(K_{i}:[a,b]\times [a,b]\times \mathbb {R}^n\rightarrow \mathbb {R}^n\) is a given mapping for each \(i=1,2,3,4\). For this intention we establish common fixed point results for two pairs of weakly compatible mappings satisfying the contractive condition of rational type in the frame work of complex valued 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.

In this work, we introduce the concept of a cyclic compatible contraction and prove related fixed point theorems in the generating space of a b-quasi-metric family.

A split system on a finite set X is a set of bipartitions of X. Weakly compatible and k-compatible (k≥1) split systems are split systems which satisfy special restrictions on all subsets of a certain fixed size. They arise in various areas of applied mathematics such as phylogenetics and multi-commodity flow theory. In this note, we show that the number of splits in a 3-compatible, weakly compatible split system on a set X of size n is linear in n.

n this paper, we introduce the notion of $\phi$-weakly compatible mapping for a pair of mappings. A fixed point theorem for two pairs of $\phi$-weakly compatible mappings satisfying a rational type contraction in a normed space is also established. Subsequently we use our result to find existence of solutions of variational inequalities.

Common fixed point results for new classes of noncommuting selfmaps satisfying generalized I-contraction or I-nonexpansive type conditions are established. We apply them to obtain several invariant approximation results which unify, extend, and complement the well-known results.

The aim of this article is to present, improve and generalize some recent coincidence and coupled coincidence point results from several papers in the framework of partially ordered b-metric spaces. Two examples are also provided to support the superiority of the obtained results.

Recently, Pathak [13] has made an extension of the notion of compatibility to weak compatibility, and extended the coincidence theorem for compatible mappings in Kaneko and Sessa [11] to weakly compatible mappings [13]. In the present paper, we define a new class of weakly compatible mappings (Definition 4) and prove some common fixed point theorems for these mappings, which satisfy Condition (2) below. Although our main theorem is formulated for weakly compatible mappings, its corresponding formulation for commutative mappings is also a new result, thus presenting a generalization of some theorems of Fisher, Das and Naik, Khan and Kubiaczyk, Reich, Ciric and Rhoades and Watson.

In this paper, we introduce a new twice power type contractive condition for six self-mappings in generalized metric spaces. Using the weakly commuting and weakly compatible conditions of self-mapping pairs, the existence and uniqueness of common fixed point in complete generalized metric spaces is discussed, and a new common fixed point theorem is obtained. We also provide illustrative examples in support of our new results. Our results generalize some well-known comparable results in the literature due to Ye and Gu. MSC:47H10, 54H25, 54E50.

The aim of this paper is to prove some common fixed-point theorems for weakly compatible mappings in Menger spaces satisfying common property (E.A). Some examples are also given which demonstrate the validity of our results. As an application of our main result, we present a common fixed-point theorem for four finite families of self-mappings in Menger spaces. Our result is an improved probabilistic version of the result of Sedghi et al. [Gen. Math. 18:3-12, 2010].

The purpose of this paper is to prove a common fixed point theorem, from the class of compatible continuous maps to a larger class of maps having weakly compatible maps without appeal to continuity, which generalizes the results of Jungck [3], Fisher [1], Kang and Kim [8], Jachymski [2], and Rhoades [9].

In this paper, using the concept of common (E.A) property, we prove some common fixed point theorems for three pairs of weakly compatible self-maps satisfying a generalized weakly G-contraction condition in the framework of a generalized metric space. Our results do not rely on any commuting or continuity condition of mappings. An example is provided to support our result in nonsymmetric G-metric space.

A semigroup is called eventually regular if a power of each element is regular. Regular and group-bound semigroups are each eventually regular. A tolerance relation on an eventually regular semigroup is introduced, and Lallement's result for regular semigroups is generalized to eventually regular semigroups. Weakly compatible tolerances on semigroups are studied.

We prove several fixed point theorems on cone metric spaces in which the cone does not need to be normal. These theorems generalize the recent results of Huang and Zhang (2007), Abbas and Jungck (2008), and Vetro (2007). Furthermore as corollaries, we obtain recent results of Rezapour and Hamlborani (2008).

We obtain several fixed point theorems for hybrid pairs of single-valued and multivalued occasionally weakly compatible maps defined on a symmetric space satisfying a contractive condition of integral type. The results of this paper essentially contain every theorem on hybrid and multivalued self-maps of a metric space as a special case. Erratum http://dx.doi.org/10.1155/2008/274793