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The aim of this paper is to introduce the notion of interpolative fuzzy Z-contractive condition for a pair of self maps in a fuzzy metric space, which enlarges, unifies and generalizes the existing fuzzy contractions (by Gregori et al. [6]), contraction (by Mihet [11]), fuzzy Z-contractions (by Shukla et al. ([19]) and Tirado contraction (by Tirado [20]), which are for only one self map. Using this, we establish a unique common fixed point theorem for two self maps satisfying condition (S), which was introduced by Shukla et al. in [19] through weak compatibility. As an applications, we discuss fixed point theorem for Fredholm non-linear integral equation. The article also includes an example, which shows the validity of our results. [ABSTRACT FROM AUTHOR]

In this paper, we present a new type of contraction calledW-contraction in fuzzy metric space. Utilizing this contraction, we establish a unique fixed point theorem for self-map in the structure of fuzzy metric space which turns out to be generalization of fuzzy contraction given by Gregori et al. [8]. As an application of our result, we study the existence and uniqueness of the solution to nonlinear ordinary differential equations. The article also includes an example which shows the validity of our results. [ABSTRACT FROM AUTHOR]

In this paper direct proofs of some common fixed point results for two and three mappings under weak contractive conditions are given. Some of these results are improved by using different arguments of control functions. Examples are presented showing that some generalizations can not be obtained and also that our results are distinct from the existing ones. [ABSTRACT FROM AUTHOR]

New fixed point results for a pair of non-self mappings defined on a closed subset of a metrically convex cone metric space (which is not necessarily normal) are obtained. By adapting Assad-Kirk's method the existence of a unique common fixed point for a pair of non-self mappings is proved, using only the assumption that the cone interior is nonempty. Examples show that the obtained results are proper extensions of the existing ones. [ABSTRACT FROM AUTHOR]

Recently, Chao Wang, Jinghao Zhu, Bogko Damjanovid, Liang-gen Hu [Approximating fixed points of a pair of contractive type mappings in generalized convex metric spaces, Applied Mathematics and Computation 215 (2009) 1522-1525] proved some results for an Ishikawa type iteration process with errors, which converges to the unique common fixed point of a pair of contractive type mappings in complete generalized convex metric spaces. The aim of this paper is to consider this in the frame of abstract (cone) metric spaces. We extend some fixed point results of these mappings from complete generalized convex metric spaces to convex abstract metric spaces with the solid cone. Also, we have improved some results. Four examples are included. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we introduce the concept of a w-compatible mappings to obtain coupled coincidence point and coupled point of coincidence for nonlinear contractive mappings in cone metric space with a cone having non-empty interior. Coupled common fixed point theorems for such mappings are also proved. Our results generalize, extend and unify several well known comparable results in the literature. Results are supported by three examples. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notions of α – ψ ϕ -contractive and cyclic α – ψ ϕ -contractive mappings and establish the existence and uniqueness of fixed points for such mappings in complete metric-like spaces. The results presented here substantially generalize and extend several comparable results in the existing literature, in particular those of Karapinar and Salimi (2013). As an application, we prove new fixed point results for ψ ϕ -graphic and cyclic ψ ϕ -graphic contractive mappings. Moreover, some examples and an application to integral equations are given here to illustrate the usability of the obtained results. [ABSTRACT FROM AUTHOR]