Fixed point theorems of generalized contraction mappings on ϖ-cone metric spaces over banach algebras

Abstract

Without the assumptions of normality and solidness, we investigate some properties of cones with some semiinterior points in normed algebras, introduce two novel notions of $S$-set and $S$-number associated with every semiinterior point in the underlying cone, give a constructive example with calculations of these new quantities, study some topological characterization of the topology induced by $\varpi$-cone metric of $\varpi$-cone metric space over Banach algebra with the help of semiinterior points instead of interior points, and then generalize some fixed point theorems of contraction type mapping defined on $\varpi$-cone metric space over Banach algebra with nonnormal and nonsolid cone.