No abstract

The notion of modular metric space, being a natural generalization of classical modulars over linear spaces, was recently introduced. In this paper, we introduce a generalized F-contraction in modular metric space and investigate the existence of fixed points for such contractions. As applications, we derive some new fixed point theorems in partially ordered modular metric spaces, Suzuki type fixed point theorems in modular metric spaces and fixed point theorems for contractions involving integral inequalities. Moreover, we deduce new fixed point results in triangular fuzzy metric spaces and provide some examples to illustrate the usability of the obtained results.

In the present paper, we introduce the notion of α-type F-τ-contraction and establish related fixed point results in metric spaces. An example is also given to illustrate our main results and to show that our results are proper generalization of Altun et al. (2015), Miank et al. (2015), Altun et al. (2016) and Olgun et al. (2016). We also obtain fixed point results in the setting of partially ordered metric spaces. Finally, an application is given to set up the existence of positive definite solution of non-linear matrix equation.

In this paper, we set up an adequate condition for the presence of a solution of the nonlinear matrix equation. To do so, we prove the existence of fixed points for multi-valued modified F-contractions in the context of complete metric spaces, which generalize, refine, and extend several existing results in the literature. An example is accompanies the obtained results to show that derived results are a proper generalization.

In this paper, we introduce the concepts of multivalued cyclic α-F contraction and triangular α-orbital admissible mappings. We use these concepts to find global best approximation solutions in a metric space with proximally complete property. We also provide some nontrivial examples to support our results. As an application, we obtain best proximity point results in partially ordered metric spaces and best proximity point theorems for single-valued mappings. We also prove fixed point results for multivalued and single-valued α-type F-contractions.