In this article, we introduce the generalized multi-quadratic mappings and then describe them as a equation. As a special case of such mappings, we study the Hyers-Ulam stability of multi-quadratic mappings in non-Archimedean spaces by applying a fixed point theorem. Moreover, we prove that such mappings can be hyperstable.

In this paper, the existence of fixed point for Pata type Zamfirescu mapping in a complete metric space is proved. Our result give existence of fixed point for a wider class of functions and also prove the existence of best proximity point to the result on “A fixed point theorem in metric spaces”, given by vittorino Pata.

In this paper, we introduce the concepts of an orthogonal $ F $-contractive type mapping, an orthogonal Kannan $ F $-contractive type mapping and an orthogonal $ F $-expanding type mapping. We prove some fixed point theorems for these mappings in orthogonal complete $ b $-metric spaces. The obtained results generalize and extend some of the well known results in the literature. An example is presented to support our results.

The purpose of this paper is to introduce the notion of generalized multivalued $\left(\psi ,\varphi \right)$-type contractions and generalized multivalued $\left(\psi ,\varphi \right)$-type Suzuki contractions and establish some new common fixed point theorems for such multivalued mappings in complete metric spaces. Our results are extension and improvement of the Suzuki and Nadler contraction theorems, Jleli and Samet, Piri and Kumam, Mizoguchi and Takahashi, and Liu et al. fixed point theorems. We provide an example for supporting our new results. Moreover, an application of our main result to the existence of solution of system of functional equations is also presented.