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In this paper, we investigate the existence and uniqueness of a fixed point of almost contractions via simulation functions in metric spaces. Moreover, some examples and an application to integral equations are given to support availability of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of generalized almost rational contraction with respect to a pair of self mappings on a complete metric space. Several common fixed point results for such mappings are proved. Our results extend and unify various results in the existing literature. An example and application to obtain the existence of a common solution of the system of functional equations arising in dynamic programming are also given in order to illustrate the effectiveness of the presented results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of generalized weakly α-contractive mappings and give some common fixed point results for this type of contraction. The presented theorems extend, generalize and improve many existing results in the literature. Two examples as well as an application to ordinary differential equations are also given in order to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]