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- Title
An Extended Kannan Contraction Mapping and Applications.
- Authors
Pant, R. P.
- Abstract
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.
- Subjects
FIBONACCI sequence; NONEXPANSIVE mappings; DIOPHANTINE equations; NONLINEAR equations; TRIANGLES
- Publication
International Journal of Mathematical, Engineering & Management Sciences, 2024, Vol 9, Issue 4, p931
- ISSN
2455-7749
- Publication type
Article
- DOI
10.33889/IJMEMS.2024.9.4.049