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

Deepak Singh, Manoj Ughade, Alok Kumar, Manoj Kumar Shukla

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.

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Published: 2024-01-25

How to Cite this Article:

Deepak Singh, Manoj Ughade, Alok Kumar, Manoj Kumar Shukla, Fixed points of Kannan and Reich interpolative contractions in controlled metric spaces, Adv. Fixed Point Theory, 14 (2024), Article ID 6

Copyright © 2024 Deepak Singh, Manoj Ughade, Alok Kumar, Manoj Kumar Shukla. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Advances in Fixed Point Theory

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