# 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

, Volume 112 (2) – Mar 21, 2017
12 pages

/lp/springer_journal/modified-halpern-s-iteration-for-fixed-point-theory-of-a-finite-family-5xzCTWGKao
Publisher
Springer Milan
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

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