FIXED POINT THEOREMS AND CONVERGENCE THEOREMS FOR SOME GENERALIZED NONEXPANSIVE MAPPINGS

By Tomonari Suzuki. 2008

498 citations recorded by the source corpus.

We introduce some condition on mappings. The condition is weaker than nonexpansiveness and stronger than quasinonexpansiveness. We present fixed point theorems and convergence theorems for mappings satisfying the condition.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/bd18950dc98682bcda896f6eb3700a5804fbc506

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Ali Abkar
2. M. Eslamian
3. Naseer Shahzad
4. W. Inthakon
5. Rajendra Pant
6. Muhammad Arshad
7. R. Haghi
8. A. Kaewkhao

In Geometry and Topology

1. Ali Abkar
2. M. Eslamian
3. Naseer Shahzad
4. R. Haghi
5. W. Inthakon
6. Rajendra Pant
7. Muhammad Arshad
8. A. Kaewkhao

In Numerical Analysis

1. W. Inthakon
2. Rajendra Pant
3. Muhammad Arshad
4. Ali Abkar
5. R. Haghi
6. A. Kaewkhao
7. Naseer Shahzad
8. Sh. Rezapour

Citations in the corpus

• Numerical reckoning fixed points for Suzuki’s generalized nonexpansive mappings via new iteration process (2018, background): “Suzuki [21] obtained fixed point theorems and convergence theorems for Suzuki generalized nonexpansive mappings.”
• Approximating fixed points of enriched nonexpansive mappings by Krasnoselskij iteration in Hilbert spaces (2019, background): “As a consequence, various single-valued and multi-valued self and nonself mappings related to nonexpansive mappings were introduced and studied independently of in connection to nonexpansive mappings (see MathScinet or zbMATH): quasi-nonexpansive mappings (see [40]), strictly quasi-nonexpansive mapp”
• Edelstein's method and fixed point theorems for some generalized nonexpansive mappings (2009, methodology): “Suzuki also showed in [19] that every nonexpansive mapping satisfies condition (C) but the converse is not true.”
• Approximating Fixed Points of Generalized α-Nonexpansive Mappings in Banach Spaces (2017, background): “Now a natural question arises that does there exists a class of mapping, which contains both the Suzuki-type generalized nonexpansive mappings and α-nonexpansive mappings?”
• Common fixed point results in CAT(0) spaces (2011, background): “In 2008, Suzuki [8] introduced a condition which is weaker than nonexpansiveness and stronger than quasinonexpansiveness.”
• Some fixed point generalizations are not real generalizations (2011, result): “Recently, Suzuki [11] proved the following theorem that generalizes the results of Browder [12,13] and Göhde [14].”