in this paper, the notion of $psi -$weak contraction cite{rhoades} isextended to fuzzy metric spaces. the existence of common fixed points fortwo mappings is established where one mapping is $psi -$weak contractionwith respect to another mapping on a fuzzy metric space. our resultgeneralizes a result of gregori and sapena cite{gregori}.

in this paper, a concept of generalized weakly contraction mappings in partially ordered fuzzy metric spaces is introduced and  coincidence point  theorems on partially ordered fuzzy metric spaces are proved. also, as the corollary of these theorems, some common fixed point theorems on partially ordered fuzzy metric spaces are presented.

We consider a new iterative method due to Kadioglu and Yildirim (2014) for further investigation. We study convergence analysis of this iterative method when applied to class of contraction mappings. Furthermore, we give a data dependence result for fixed point of contraction mappings with the help of the new iteration method.

We introduce the concept of mixed (G,S)-monotone mappings and prove coupled coincidence point theorems for such mappings satisfying a nonlinear contraction involving altering distance functions. Presented theorems extend, improve and generalize the recent results of Harjani, López and Sadarangani [J. Harjani, B. López and K. Sadarangani, Fixed point theorems for mixed monotone operators and app...

Abstract In this paper we introduce some new types of contractive mappings by combining Caristi contraction, ?iri?-quasi contraction and weak in the framework a metric space. We prove fixed point theorems for such type over complete spaces with help ? -diminishing property. Some examples are given strengthening hypothesis our established theorems.

In this paper, we describe some topological properties of dualistic partial metric spaces and establish some fixed point theorems for weak contraction mappings of rational type defined on dual partial metric spaces. These results are generalizations of some existing results in the literature. Moreover, we present examples to illustrate our result.

In this study, we introduce a new definition called δ-contraction. However, prove some theorems for mappings satisfying the δ-contraction and touch upon fixed points. obtained theorems, also show existence uniqueness of order to validity results our main give few examples as well an application that reveals solution integral equations.