Recent Developments of Cone metric spaces over Banach algebra

The book comprises of seven chapters.Chapter 1 we present some preliminaries that will be needed in the sequel.Chapter 2 we introduce the notion of partial cone metric spaces over Banach algebra and prove fixed point results.Chapter 3 we propose a generalization called partial cone b-metric spaces over Banach algebra, replacing Banach spaces by Banach algebra.In Chapter 4 we define J-cone metric spaces over Banach algebra. We study the topological and structural properties of the new space and derive some fixed point theorems.In Chapter 5 we establish some coupled fixed point results for generalized Lipschitz mappings verifying in J-cone metric space over Banach algebra.Chapter 6 we introduce the concept of cone b_2-metric space over Banach algebra. Next, we define generalized Lipschitz and expansive maps in the new structure and establish the existence and uniqueness of fixed points for such mappings.In Chapter 7 we devote our study to introduce the structure of N-cone metric space over Banach algebra. We define generalized Lipschitz mapping and prove some fixed point results for such mappings in the new framework.