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

Original Paper


The aim of this research is to introduce GS-mapping generated by a finite family of G-nonexpansive mappings and finite real numbers and prove a convergence theorem of Halpern iteration associated with GS-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 \(\pi \) using our theorem.


G–S-mapping G-nonexpansive mapping Dominating set 

Mathematics Subject Classification

47H09 47H10 05C69 



This research was supported by Research Administration Division of King Mongkut\(^{,}s\) Institute of Technology Ladkrabang.


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Copyright information

© Springer-Verlag Italia 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceKing Mongkut’s Institute of Technology LadkrabangBangkokThailand

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