In this paper, we shall generalize the definition of (φ− k) −B contraction to multi-valued mappings which was presented before in single valued case by Mihet. Then we shall prove two fixed point theorems for multi-valued (φ− k) − B contraction mappings in probabilistic metric space.

In this paper , we obtain two common fixed point theorems one for two pairs of single and set-valued mappings and another for four set-valued mappings satisfying integral type conditions.

In this paper, we introduce the Denjoy-Pettis integral of set-valued mappings and investigate some properties of the set-valued Denjoy-Pettis integral. Finally we obtain the Dominated Convergence Theorem and Monotone Convergence Theorem for set-valued DenjoyPettis integrable mappings.

Abstract This paper aims to present the concept of multi-valued mappings in fuzzy cone metric spaces and prove some basic lemmas, a Hausdorff metric, fixed point results for set-valued cone-contraction mappings. We theorem rational type cone-contractions spaces. Our extend improve given literature.

The notion of compatibility for point-to-point mappings recently defined by Jungck is generalized to include multi-valued mappings. This idea is used to establish a fixed point theorem for a generalized contractive multi-valued mapping and a single-valued napping.