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Convergent point of G-type nonexpansive mapping with graph

D.P. Shukla1 , Vivek Tiwari2

  1. Fixed point,G-nonexpansive mappings, Abbas et al., Banach space, directed graph.

Section:Research Paper, Product Type: Isroset-Journal
Vol.5 , Issue.5 , pp.179-184, Oct-2018


CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i5.179184


Online published on Oct 31, 2018


Copyright © D.P. Shukla , Vivek Tiwari . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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IEEE Style Citation: D.P. Shukla , Vivek Tiwari, “Convergent point of G-type nonexpansive mapping with graph,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.5, pp.179-184, 2018.

MLA Style Citation: D.P. Shukla , Vivek Tiwari "Convergent point of G-type nonexpansive mapping with graph." International Journal of Scientific Research in Mathematical and Statistical Sciences 5.5 (2018): 179-184.

APA Style Citation: D.P. Shukla , Vivek Tiwari, (2018). Convergent point of G-type nonexpansive mapping with graph. International Journal of Scientific Research in Mathematical and Statistical Sciences, 5(5), 179-184.

BibTex Style Citation:
@article{Shukla_2018,
author = {D.P. Shukla , Vivek Tiwari},
title = {Convergent point of G-type nonexpansive mapping with graph},
journal = {International Journal of Scientific Research in Mathematical and Statistical Sciences},
issue_date = {10 2018},
volume = {5},
Issue = {5},
month = {10},
year = {2018},
issn = {2347-2693},
pages = {179-184},
url = {https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=885},
doi = {https://doi.org/10.26438/ijcse/v5i5.179184}
publisher = {IJCSE, Indore, INDIA},
}

RIS Style Citation:
TY - JOUR
DO = {https://doi.org/10.26438/ijcse/v5i5.179184}
UR - https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=885
TI - Convergent point of G-type nonexpansive mapping with graph
T2 - International Journal of Scientific Research in Mathematical and Statistical Sciences
AU - D.P. Shukla , Vivek Tiwari
PY - 2018
DA - 2018/10/31
PB - IJCSE, Indore, INDIA
SP - 179-184
IS - 5
VL - 5
SN - 2347-2693
ER -

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Abstract :
In this paper, we prove some weak and strong convergence of a sequence {x_n} generated by the Abbas at el. techniques to some common fixed points of G-type nonexpansive mappings defined on Banach space with graph.

Key-Words / Index Term :
Fixed point,G-nonexpansive mappings, Abbas et al., Banach space, directed graph

References :
[1] Jachymski, J: The contraction principle for mappings on a metric space with a graph. Proc. Am. Math. Soc.136, 1359-1373 (2008).
[2] Aleomraninejad, SMA, Rezapour, S, Shahzad, N: Some fixed point result on a metic space with a graph. Topol. Appl. 159, 659-663 (2012).
[3] Alfuraidan, MR, Khasmi, MA: Fixed points of monotone nonexpansive mappings on a hyperbolic metric space with a graph. Fixed point theory Appl. (2015).
[4] Alfuraidan, MR: Fixed points of monotone multivalued mappings on a metic space with a graph J. inequal. Appl. (2015).
[5] Alfuraidan, MR: Fixed points of monotone nonexpansive mapping with a graph, fixed point theory Appl. (2015).
[6] Tiammee, J, Kaehao, A, Suantai, S,On Browder’s convergence theorem and Halpern iteration process for G-nonexpansive mappings in Hilbert spaces endowed with graph. Fixed point Theory Appl. (2015).
[7] Shahzad, N, Al-Dubiban, R; Approximating common fixed points of nonexpansive mappings in Banach spaces Georgian Math. J. 13 (3), 529-537 (2006).
[8] Schu, J: weak and strong convergence to fixed points of asymptotically nonexpansive mappings. Bull. Aust. Math. Soc. 43 (1), 153-159 (1991).
[9] Xu, HK: Inequalities in Banach spaces with applications. Nonlinear anal.16 (12), 1127-1138 (1991).
[10] Suantai, S: weak and strong convergence criteria of Noor iterations for asymptotically nonexpansive mappings J. Math. Anal. Appl. 331, 506-517 (2005).

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