An Extended Kannan Contraction Mapping and Applications

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We extend the Kannan contraction principle and obtain a result that holds for both contractive and non-expansive mappings. Such mappings admit multiple fixed-points and the fixed-point sets and domains of these mappings display interesting algebraic, geometric and dynamical features. Since contraction mappings admit only one fixed-point, almost all the existing results on contractive mappings can be generalized in the light of our theorem. As an application of our main theorem, we obtain the integral solutions of a nonlinear Diophantine equation; the solutions are Pythagorean triples, which represent right angled triangles, and each integer of the triple belongs to a Fibonacci type sequence. These results can be generalised to obtain integral solutions of Diophantine equations of the type (n+k)2 - n2 = p2, k > 1, and to check whether the related sequences are Fibonacci sequences.

Original languageEnglish
Pages (from-to)931-942
Number of pages12
JournalInternational Journal of Mathematical, Engineering and Management Sciences
Issue number4
Publication statusPublished - Aug 2024
Externally publishedYes


  • Contraction mappings
  • Eventual fixed points
  • Fibonacci sequence
  • Fixed points
  • Pythagorean triple

ASJC Scopus subject areas

  • General Computer Science
  • General Mathematics
  • General Business,Management and Accounting
  • General Engineering


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