Some innovative results for interpolative Kannan type and Reich-Rus-Ćirić type cyclic contractions

[EN] In this manuscript, we present innovative findings on the existence and uniqueness of fixed points for cyclic mappings. Our discussion covers results for interpolative Kannan-type cyclic contractions in two cases: when the sum of the interpolative exponents is less than one and when it is greater than one. Additionally, we provide results for interpolative Reich-Rus-Ćirić cyclic contractions specifically for cases where the sum of the interpolative exponents is greater than one. Furthermore, we verify our results with suitable examples. Our results are new and complement some results in the literature.