We propose a refinement in the interpolative approach in fixed-point theory. In particular, using this method, we prove the existence of fixed points and common fixed points for Kannan-type contractions and provide examples to support our results.

We introduce the concept of startpoint and endpoint for multivalued maps defined on a quasi-pseudometric space. We investigate the relation between these new concepts and the existence of fixed points for these set valued maps. Dedicated to my beloved Clémence on the occasion of her 25th birthday

In this article, we discuss some fixed point theorems in metric type spaces. The need to define such space came from the properties obtain on cone metric spaces and the connection between the two notions is clearly explained in [1]. In particular, we show that most of the new results are merely copies of the classic ones.

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In this research article, we propose efficient numerical iterative methods for estimating roots of interval-valued trapezoidal fuzzy nonlinear equations. Convergence analysis proves that the order of convergence of numerical schemes is 3. Some real-life applications are considered from optimization as numerical test problems which contain interval-valued trapezoidal fuzzy quantities in parametric form. Numerical illustrations are given to show the dominance efficiency of the newly constructed iterative schemes as compared to existing methods in literature.