In present paper, we prove unique fixed point theorems for contractive maps in \(N\) -cone metric spaces. Our results extend and generalize some well-known results of (Banach, Fund Math 3:133–181 1992; Chatterjee, Rend Acad Bulgare Sci 25:727–730 1972; Kannan, Bull Calcutta Math Soc 60:71–76 1968; Rezapour and Hamlbarani, J Math Anal Appl 345:719–724 2008) in the setting of \(N\) -cone metric spaces.

The aim of the article is to establish the structure of partial cone b-metric spaces over Banach algebras. Topological and structural properties are investigated of the new spaces. We also define generalized Lipschitz mappings and give their application in fixed point theory. The results presented in this paper substantially extend and strengthen the results of the literature. Few examples are provided to support our conclusions and as an application we establish the existence and uniqueness of a solution to a class of system of nonlinear integral equations.

In this paper, we introduce the M-cone metric space over Banach algebra as a generalization of both M-metric space and cone metric space over Banach algebra and investigate some fixed point results in the new settings. Some examples are presented as illustrations. Finally, the results are supported by an application to examine the existence and uniqueness of solution for a Fredholm integral equation.