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 \(\pi \) using our theorem.
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Acknowledgements
This research was supported by Research Administration Division of King Mongkut\(^{,}s\) Institute of Technology Ladkrabang.
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Kangtunyakarn, A. Modified Halpern’s iteration for fixed point theory of a finite family of G-nonexpansive mappings endowed with graph. RACSAM 112, 437–448 (2018). https://doi.org/10.1007/s13398-017-0390-y
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DOI: https://doi.org/10.1007/s13398-017-0390-y