Revisiting the Kannan Type Contractions via Interpolation
By E. Karapınar. Advances in the Theory of Nonlinear Analysis and its Application, 2018
222 citations recorded by the source corpus.
In the paper, we revisited the well-known fixed point theorem of Kannan under the aspect of interpolation. By using the interpolation notion, we propose a new Kannan type contraction to maximize the rate of convergence.
Subfields: Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/e7de5aebac58eac9281350ac49dec0deb239d8c4
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In Geometry and Topology
- Hassen Aydi
- E. Karapınar
- A. F. Roldán López de Hierro
- Chi-Ming Chen
- Inci M. Erhan
- Stojan Radenovic
- Zoran Kadelburg
- Wasfi A. Shatanawi
Citations in the corpus
- A Solution for Volterra Fractional Integral Equations by Hybrid Contractions (2019, unknown): “If p = 0 and σ1 = 0, σ2 = δ, σ3 = 1 − δ, σ4 = 0, we get an interpolative contraction of Kannan type: d(TΩ, Tω) ≤ κ(d(Ω, TΩ))(d(ω, Tω))1−δ, for all Ω, ω ∈ X\zT(X), where κ ∈ [0, 1), see [6].”
- ω-Interpolative Ćirić-Reich-Rus-Type Contractions (2019, background): “Let T be a self-mapping on X defined by: Tx = { 3 2 , if x ∈ [1, 2] 1 3 , if x ∈ [0, 1).”
- Interpolative Ćirić-Reich-Rus Type Contractions via the Branciari Distance (2019, background): “In 2018, Karapınar [5] considered Theorem 1 concerning interpolation theory.”
- Interpolative Reich–Rus–Ćirić Type Contractions on Partial Metric Spaces (2018, unknown): “Very recently, in [2], the acclaimed theorem of Kannan was revisited by taking the interpolation theory into account.”