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June 14, 2026Journal of Function Spaces0 citationsOpen Access

Major Remark on Unique Fixed‐Point Theorems via Interpolative and Rational Contractions in Super Metric Spaces and A New Approach to the Interpolative Contractions

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AAArslan Hojat AnsariANAli Mohammad NazariSPSeyyed Hossein Jafari Petroudi

Key Points

  • This analysis questions the originality of certain fixed-point theorems related to interpolative contractions and highlights flaws in their proofs.
  • Analyzed recent fixed-point results concerning interpolative and rational contractions in super metric spaces.
  • Identified issues in proofs associated with power-type inequalities on the interval (0, 1).
  • Discussed reformulation strategies to enhance the validity of certain theorems.
  • Certain fixed-point theorems were shown to derive from established principles, lacking genuine novelty.
  • Recurring proof issues were identified, affecting the validity of several interpolative contraction results.
  • Recommendations for improved formulations of some theorems were discussed in light of identified issues.

Abstract

This paper presents a critical analysis of several recent fixed‐point results involving interpolative and rational contractions in super metric spaces and related frameworks. We first show that certain claimed fixed‐point theorems, including a result concerning ( ρ , λ )‐interpolative Kannan contractions, do not provide genuinely new contributions, since they can be derived directly from previously established principles. Furthermore, we examine a number of other interpolative contraction theorems and identify a recurring issue in their proofs arising from the improper use of power‐type inequalities on the interval (0, 1). This observation indicates that the corresponding fixed‐point arguments cannot be concluded under the stated assumptions. We also briefly discuss possible ways to reformulate some of these results under additional conditions that may restore their validity. Our analysis is aimed at clarifying the current state of research on interpolative contractions and at highlighting the necessity of greater care in the formulation and verification of such results.

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Cite This Study

Ansari et al. (2026) studied this question.

synapsesocial.com/papers/6a2e47cdb1cc60ccdea8c3b2https://doi.org/10.1155/jofs/1157040
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