Common Invariant Point Consequences with Jungck Contractive Situations and Cyclic Representations in Complete Spaces

Abstract

The functional contractions for the cyclic maps may be seen as the functions involving multiple maps or spaces that comply with a contraction-like situation in a cyclic manner. Despite underpinning on a single distance space, a cyclical contraction is a more specialized variant, often employed in the multi-variable invariant point problems like in optimization, differential equations, or control theory. Invigorated with the work, Kirk, [12] and of other synchronous researchers/authors, we wish to propose some cyclic representations (functions), in such versions, that are other than previously proposed. These mappings may be called co-cyclic or sometimes sub-cyclic. Furthermore, introducing the notion of equivalent sequences along with some supportive as well as suitable illustrations, we state and then prove the associated common invariant point propositions, which exist uniquely, in the complete distance spaces.