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The aim of this paper is to introduce new notions called generalized [Formula: see text] contraction and rational type [Formula: see text] contraction for hybrid maps in complete G-metric spaces. First, using new concept of generalized [Formula: see text] contraction we establish a common fixed point theorem for a hybrid pair of weakly compatible maps. Second, we prove a common fixed point theorem for occasionally coincidentally idempotent mappings satisfying another new concept of rational type [Formula: see text] contraction under common limit range property. Our results generalize and improve several known results of the existing literature. Also, we give an example to indicate the usefulness of our main results.

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.

In this paper, we consider weakly compatible mappings with respect to a generalized $$c$$-distance in cone $$b$$-metric spaces and obtain new common fixed-point theorems. Our results provide a more general statement, since we need not to nor the continuity of mappings and nor the normality of cone. In particular, we refer to the results of M. Abbas and G. Jungck [Common fixed point results for non-commuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl. 341 (2008) 416–420]. Some corollaries and examples are presented to support the main result proved herein.

In this paper, a new type of contraction for several self-mappings of a metric space, called FM-contraction, is introduced. This extends the one presented for a single map by Wardowski [Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012:94, 2012]. Coincidence and common fixed point of eight self mappings satisfying FM-contraction conditions are established via common limit range property without exploiting the completeness of the space or the continuity of the involved maps. Coincidence and common fixed point of eight self-maps satisfying FM-contraction conditions via the common property (E.A.) are also studied. Our results generalize, extend and improve the analogous recent results in the literature, and some examples are presented to justify the validity of our main results.

In this paper, we establish coincidence point and common fixed point theorems involving two pairs of weakly compatible mapping satisfying contraction condition with complex coefficient are proved in complex valued metric space. The presented theorems generalize, extend and improve many existing results in the literature. An example is given at the end of the paper.

In this paper, we prove a common xed point theorem for weakly compatible mappings in complex valued b-metric space and also improve the condition of contraction of the results of M. Kumar et al.[7]. Further, we prove common xed point theorems for weakly compatible mappings with (E.A.) property and (CLRg) property.

Coupled fixed point problems have attracted much attention in recent times. The aim of this paper is to extend the notions of E.A. property, CLR property and JCLR property for coupled mappings in Menger metric space and use this notions to generalizes the recent results of Jian-Zhong Xiao. The main result is supported by a suitable example.

In this paper, we prove the existence of a coincident point and a common xed point for two self mappings dened

In this article, we establish some common fixed point theorems for two pairs of weakly compatible mappings with (E. A.) and (CLR) property in dislocated metric space which generalize and extend some similar results in the literature.

In this article, we establish some new results on Jungck-Ćirić-Wardowski type mappings in complete metric spaces. Using our new approach, the conditions (W2) and (W3) of Wardowski do not apply for the proof of Cauchyness of the Picard-Jungck sequence. Our results generalize, improve and complement several results in the existing literature.

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.

We present fixed point results of mappings satisfying generalized contractive conditions in complex valued metric spaces. As an application, we obtain a common fixed point of a pair of weakly compatible mappings. Some common fixed point results of generalized contractive-type mappings involved in cocyclic representation of a nonempty subset of a complex valued metric space are also obtained. Some examples are also presented to support the results proved herein. These results extend and generalize many results in the existing literature.

The aim of this paper is to obtain some new integral type fixed point theorems for nonself weakly compatible mappings in symmetric spaces satisfying generalized(ψ,φ)-contractive conditions employing the common limit range property. We furnish some interesting examples which support our main theorems. Our results generalize and extend some recent results contained in Imdad et al. (2013) to symmetric spaces. Consequently, a host of metrical common fixed theorems are generalized and improved. In the process, we also derive a fixed point theorem for four finite families of mappings which can be utilized to derive common fixed point theorems involving any number of finite mappings.

Common fixed point theorems for two pairs of mappings are proved in dislocated fuzzy metric space using horizontally weak compatibility condition. Our results extends and generalises many existing fixed point theorems.

In this paper, we will show the properties of common fixed point for three functions on contraction mapping and expansive mapping by using the coincidence point property and weakly compatible function property. However, we also show the sufficient condition without applying the weakly compatible function property.

The purpose of this paper is to prove the existence of the unique common fixed point theorems of a pair of weakly compatible mappings satisfying $\Phi$-maps in modular G-metric spaces.

In the present paper, we utilize the notion of conversecommuting mappings due to Lu [On common xed points for con-verse commuting self-maps on a metric spaces, Acta. Anal. Funct.Appl. 4(3) (2002), 226-228] and prove a common xed point the-orem in Menger space using an implicit relation. We also give anillustrative example to support our main result. 1. IntroductionIn 1986, Jungck [9] introduced the notion of compatible mappings inmetric space. Most of the common xed point theorems for contractionmappings invariably require a compatibility condition besides assumingcontinuity of at least one of the mappings. Later on, Jungck and Rhoades[10] studied the notion of weakly compatible mappings and utilized itas a tool to improve commutativity conditions in common xed pointtheorems. Many mathematicians proved several xed point results inMenger spaces (see [2, 3, 4, 6, 7, 8, 16, 18, 19, 20, 25]). In 2002, Lu [13]presented the concept of the converse commuting mappings, as a reverseprocess of weakly compatible mappings and proved common xed pointtheorems for single-valued mappings in metric spaces (also see [14]).Recently, Pathak and Verma [21, 22] and Chugh et al. [5] proved some xed point theorems for converse commuting mappings.In 1998, Popa and Turko glu [24] proved some xed points theoremfor hybrid mappings by using an implicit relation. Popa used the familyof implicit real functions and proved common xed point theorems (alsosee, [23]).

We prove some common fixed point theorems for two pairs of weakly compatible mappings satisfying a rational type contractive condition in the framework of complex valued metric spaces. The proved results generalize and extend some of the known results in the literature.

In this paper, weakly compatible and occasionally weakly compatible mappings are discussed in detailed and generalized common fixed point theorems of two and four mappings are proved in metric space with implicit function. Our results extends and generalists many well known results.

The main purpose of this paper is to obtain common fixed point theorem for weakly compatible mappings in generalisation symmetric spaces and a Property (E.A) introduced in (M. Aamri, D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl. 270 (2002) 181-188). Our theorem generalizes theorems Duran turkoglu and ishak altun, a common fixed point theorem for weakly compatible mappings in symmetric spaces satisfying Bol. Soc. Mat. Mexicana (3) Vol. 13, 2007.

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.

In the present paper, we prove common fixed point theorems for single-valued and set-valued occasionally weakly compatible mappings in Menger spaces. Our results improve and extend the results of Chen and Chang (Chi-Ming Chen and Tong-Huei Chang, Common fixed point theorems in Menger spaces, Int. J. Math. Math. Sci. 2006 (2006), Article ID 75931, Pages 1-15).

In this paper, we prove a common fixed point theorem for a pair of weakly compatible mappings in fuzzy metric space using the joint common limit in the range property of mappings called (JCLR) property. An example is also furnished which demonstrates the validity of main result. We also extend our main result to two finite families of self mappings. Our results improve and generalize results of Cho et al. [Y. J. Cho, S. Sedghi and N. Shobe, “Generalized fixed point theorems for compatible mappings with some types in fuzzy metric spaces,” Chaos, Solitons & Fractals, Vol. 39, No. 5, 2009, pp. 2233-2244.] and several known results existing in the literature.

We prove some common fixed point theorems in probabilistic semi-metric spaces for families of occasionally weakly compatible mappings. We also give a common fixed point theorem for mappings satisfying an integral-type implicit relation.

We prove the existence of common fixed points for two weakly compatible mappings satisfying a ?generalized condition (B)?. This result generalizes some theorems of Al-Thagafi and Shahzad [2] and Babu, Sandhya and Kameswari [3].

A general common fixed point theorem for two pairs of occasionally weak compatible expansive mappings satisfying a significantly enriched implicit function is proved in symmetric spaces which generalizes several previously known results. Some related results and illustrative examples are also discussed.

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.

In this paper, we obtain some common fixed point theorems for occasionally weakly compatible mappings on a set X together with the function d : X × X → [ 0 , ∞ ) without using the triangle inequality and assuming symmetry only on the set of points of coincidence.

The purpose of this paper is to establish common fixed point theorems for set-valued mappings between 2-metric spaces. Generalizations of some definitions in 2-metric spaces and theorems by Ahmed [Ahmed MA. Common fixed point theorems for weakly compatible mappings. Rocky Mt J Math 2003;33 (4):1189–203.], generalized of Fisher [Fisher B. Common fixed points of mappings and set-valued mappings on a metric spaces. Kyungpook Math J 1985;25:35–42.] in 2-metric spaces.

Some new theorems on random coincidence points and random fixed points for weakly compatible mappings in convex separable complete metric spaces have been established. These results generalize some recent well known comparable results in the literature.

We present coincidence points and common fixed point re- sults for (f, g)-contractive mapping and (f, g)-nonexpansive mappings. Our results generalize and complement various known results existing in the literature.

In this paper, we prove a common fixed point theorem for multi valued mappings under the condition of weak compatibility. Also, we define compatible maps of type (I) for multi valued mappings and prove a common fixed point theorem for this type mappings. We use an implicit relation to prove our main theorems.

We prove common fixed point theorems for four mappings satisfying implicit relations in symmetric spaces using the concept of occasionally weakly compatible mappings. Our Theorems generalize results of [1], [3], [4] and [7]. .