Fixed points of Kannan and Reich interpolative contractions in controlled metric spaces

Abstract

In this paper, we introduce (𝜆, 𝛼)-interpolative Kannan contraction, (𝜆, 𝛼, 𝛽)-interpolative Kannan contraction and (𝜆, 𝛼, 𝛽, 𝛾)-interpolative Reich contraction. Also, we establish some fixed-point theorems in complete controlled metric spaces. Additionally, these theorems expand and apply a number of intriguing findings from metric fixed-point theory to the controlled metric setting.