Modified Halpern’s iteration for fixed point theory of a finite family of G-nonexpansive mappings endowed with graph

Modified Halpern’s iteration for fixed point theory of a finite family of G-nonexpansive... The aim of this research is to introduce G–S-mapping generated by a finite family of G-nonexpansive mappings and finite real numbers and prove a convergence theorem of Halpern iteration associated with G–S-mapping for fixed point problem of a finite family of G-nonexpansive mapping in Hilbert spaces endowed with graph, which extends the work of Tiammee et al. (Fixed Point Theory Appl. 2015:187, 2015). Moreover, we introduce a new method for the estimation of value of $$\pi $$ π using our theorem. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Springer Journals

Modified Halpern’s iteration for fixed point theory of a finite family of G-nonexpansive mappings endowed with graph

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Publisher
Springer Milan
Copyright
Copyright © 2017 by Springer-Verlag Italia
Subject
Mathematics; Mathematics, general; Applications of Mathematics; Theoretical, Mathematical and Computational Physics
ISSN
1578-7303
eISSN
1579-1505
D.O.I.
10.1007/s13398-017-0390-y
Publisher site
See Article on Publisher Site

Abstract

The aim of this research is to introduce G–S-mapping generated by a finite family of G-nonexpansive mappings and finite real numbers and prove a convergence theorem of Halpern iteration associated with G–S-mapping for fixed point problem of a finite family of G-nonexpansive mapping in Hilbert spaces endowed with graph, which extends the work of Tiammee et al. (Fixed Point Theory Appl. 2015:187, 2015). Moreover, we introduce a new method for the estimation of value of $$\pi $$ π using our theorem.

Journal

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. MatemáticasSpringer Journals

Published: Mar 21, 2017

References

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