In this paper, the idea of MA-simulation function is introduced which has further been utilized to establish new fixed point results in fuzzy metric spaces. Moreover, it is shown that the proven result is quite a unified one to generalize several existing result. Furthermore, some new results are established to show the utility of our results. Some illustrative examples are also given which exhibit the usability of our results. Finally, we provide an application of our main results.

In this study, we introduce fuzzy weak -contraction and Suzuki-type fuzzy weak -contraction and employ these to prove some fuzzy fixed point results for fuzzy mappings in the setting of metric spaces, which is followed by an example to support our claim. Next, we deduce some corollaries and fixed point results for multivalued mappings from our main result. Finally, as an application of our result, we provide the existence of a solution for a Fredholm integral inclusion.

In this paper, the notion of ${\theta }^{*}$-weak contraction is introduced, which is utilized to prove some fixed point results. These results are helpful to give a positive response to certain open question raised by Kannan and Rhoades on the existence of contractive definition which does not force the mapping to be continuous at the fixed point. Some illustrative examples are also given to support our results. As applications of our result, we investigate the existence and uniqueness of a solution of non-linear matrix equations and integral equations of Volterra type as well.

In this paper, by introducing the concept of generalized Ćirić-type weak $({\varphi }_g,\mathcal{R})$ -contraction, we prove some common fixed point results in partial metric spaces endowed with binary relation $\mathcal{R}$ . We also deduce some useful consequences showing the usability of our results. Finally, we present an application to establish the solution of a system of integral equations.

In this paper, the notion of θ∗-weak contraction is introduced, which is utilized to prove some fixed point results. These results are helpful to give a positive response to certain open question raised by Kannan [Amer. Math. Monthly 76:1969] and Rhoades [Contemp. Math. 72:1988] on the existence of contractive definition which does not force the mapping to be continuous at the fixed point. Some illustrative examples are also given to support our results. As applications of our result, we investigate the existence and uniqueness of a solution of non-linear matrix equations and integral equations of Volterra type as well.