In this study, we develop the concept of multivalued Suzuki-type θ-contractions via a gauge function and established two new related fixed point theorems on metric spaces. We also discuss an example to validate 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.

The aim of this paper is to introduce some new fixed point results of Hardy-Rogers-type for $\alpha $-$\eta $-$GF$-contraction in a complete metric space. We extend the concept of $F$-contraction into an $\alpha $-$\eta $-$GF$-contraction of Hardy-Rogers-type. An example has been constructed to demonstrate the novelty of our results.