(Last update: 3rd Aug 2022)

# Latest results

• Koji Aoyama and Masashi Toyoda, Mean convergence theorems with respect to attractive points in a Hilbert space, arXiv:2205.11045 [math.FA].
• Koji Aoyama, A quasinonexpansive extension of a mapping with an attractive point in a Hilbert space, arXiv:2202.01419 [math.FA].

# Papers

1. Koji Aoyama and Masashi Toyoda, Fixed point theorem for a Meir-Keeler type mapping in a metric space with a transitive relation, Transylvanian Journal of Mathematics and Mechanics 14 (2022), no. 1, 1-9.
2. Koji Aoyama and Masashi Toyoda, Approximation of zeros of an accretive operator and fixed points of nonexpansive mappings in a Banach space, Linear and Nonlinear Analysis 6 (2020), no. 2, 303--313.
3. Koji Aoyama and Fumiaki Kohsaka, Strongly quasinonexpansive mappings, III, Linear and Nonlinear Analysis 6 (2020), no. 1, 1-12.
4. Koji Aoyama and Masashi Toyoda, Approximation of common fixed points of strongly nonexpansive sequences in a Banach space, Journal of Fixed Point Theory and Applications, Volume 21, Issue 1, (2019) 21:35. (DOI: 10.1007/s11784-019-0670-6) PDF
5. Koji Aoyama and Kei Zembayashi, Strongly quasinonexpansive mappings, II, Journal of Nonlinear and Convex Analysis, 19 (2018), no. 10, 1655-1663. (Proceedings of Fifth Asian Conference on Nonlinear Analysis and Optimization)
6. Koji Aoyama, Parallel hybrid methods for relatively nonexpansive mappings , Josai Mathematical Monographs 11 (2018), 121-130.
7. Koji Aoyama and Fumiaki Kohsaka, Cutter mappings and subgradient projections in Banach spaces, Linear and Nonlinear Analysis 3 (2017), no. 3, 457-473.
8. Koji Aoyama, Uniformly nonexpansive sequences, Linear and Nonlinear Analysis 3 (2017), no. 2, 179-187.
9. Koji Aoyama and Masashi Toyoda, Approximation of zeros of accretive operators in a Banach space, Israel Journal of Mathematics 220 (2017), 803-816. PDF (doi: 10.1007/s11856-017-1511-1)
10. Koji Aoyama, Viscosity approximation method for quasinonexpansive mappings with contraction-like mappings, Nihonkai Mathematical Journal 27 (2016), 168-180.
11. Koji Aoyama and Fumiaki Kohsaka, Strongly relatively nonexpansive sequences generated by firmly nonexpansive like mapping, Fixed Point Theory and Applications.2014, 2014:95, 13 pages. (doi: 10.1186/1687-1812-2014-95)
12. Koji Aoyama and Yasunori Kimura, Viscosity approximation methods with a sequence of contractions, Cubo 16 (2014), no.1, 9-20. (doi: 10.4067/S0719-06462014000100002)
13. Koji Aoyama and Fumiaki Kohsaka, Viscosity approximation process for a sequence of quasinonexpansive mappings, Fixed Point Theory and Applications.2014, 2014:17, 11 pages. (doi: 10.1186/10.1186/1687-1812-2014-17)
14. Koji Aoyama and Fumiaki Kohsaka, Uniform mean convergence theorems for hybrid mappings in Hilbert spaces, Fixed Point Theory and Applications 2012, 2012:193, 13 pages. (doi: 10.1186/1687-1812-2012-193)
15. Koji Aoyama, Yasunori Kimura, and Fumiaki Kohsaka, Strong convergence theorems for strongly relatively nonexpansive sequences and applications, Journal of Nonlinear Analysis and Optimization: Theory & Applications 3 (2012), no.1, 67-77.
16. Koji Aoyama and Fumiaki Kohsaka, Fixed point theorem for $\alpha$-nonexpansive mappings in Banach spaces, Nonlinear Analysis Series A: Theory, Methods & Applications 74 (2011), no.13, 4387-4391. (DOI: 10.1016/j.na.2011.03.057).
17. Koji Aoyama and Yasunori Kimura, Strong convergence theorems for strongly nonexpansive sequences, Applied Mathematics and Computation 217 (2011), no. 19, 7537-7545. (DOI: 10.1016/j.amc.2011.01.092).
18. Koji Aoyama and Fumiaki Kohsaka, Fixed point and mean convergence theorems for a family of $\lambda$-hybrid mappings, Journal of Nonlinear Analysis and Optimization: Theory & Applications 2 (2011), no.1, 87-95.
19. Koji Aoyama, Fumiaki Kohsaka, and Wataru Takahashi, Proximal point methods for monotone operators in Banach spaces, Taiwanese Journal of Mathematics 15 (2011), no. 1, 259-281.
20. Koji Aoyama, Shigeru Iemoto, Fumiaki Kohsaka, and Wataru Takahashi, Fixed point and ergodic theorems for $\lambda$-hybrid mappings in Hilbert spaces, Journal of Nonlinear and Convex Analysis 11 (2010), no. 2, 335-343.
21. Koji Aoyama and Fumiaki Kohsaka, Existence of fixed points of firmly nonexpansive-like mappings in Banach spaces, Fixed Point Theory and Applications 2010, Article ID 512751, 15 pages. Special Issue [Takahashi's Legacy in Fixed Point Theory].
22. Koji Aoyama, Fumiaki Kohsaka, and Wataru Takahashi, Shrinking projection methods for firmly nonexpansive mappings, Nonlinear Analysis Series A: Theory, Methods & Applications Volume 71, Issue 12 (2009), e1626-e1632. (doi: 10.1016/j.na.2009.02.001)
23. Koji Aoyama, Fumiaki Kohsaka, and Wataru Takahashi, Strongly relatively nonexpansive sequences in Banach spaces and applications, Journal of Fixed Point Theory and Applications 5 (2009), no. 2, 201-225. PDF
24. Koji Aoyama, Fumiaki Kohsaka, and Wataru Takahashi, Three generalizations of firmly nonexpansive mappings: Their relations and continuity properties, Journal of Nonlinear and Convex Analysis 10 (2009), no. 1, 131-147.
25. Masanori Akatsuka, Koji Aoyama, and Wataru Takahashi, Mean ergodic theorems for a sequence of nonexpansive mappings in Hilbert spaces, Scientiae Mathematicae Japonicae 68 (2008), no. 2, 233-239.
26. Koji Aoyama, Yasunori Kimura, and Wataru Takahashi, Maximal monotone operators and maximal monotone functions for equilibrium problems, Journal of Convex Analysis 15 (2008), no. 2, 395-409.
27. Koji Aoyama, Yasunori Kimura, Wataru Takahashi, and Masashi Toyoda, On a strongly nonexpansive sequence in Hilbert spaces, Journal of Nonlinear and Convex Analysis 8 (2007), no. 3, 471-490.
28. Koji Aoyama and Wataru Takahashi, Strong convergence theorems for a family of relatively nonexpansive mappings in Banach spaces, Fixed Point Theory 8 (2007), no.2, 143-160.
29. Koji Aoyama, Yasunori Kimura, Wataru Takahashi, and Masashi Toyoda, Approximation of common fixed points of a countable family of nonexpansive mappings in a Banach space, Nonlinear Analysis Series A: Theory, Methods & Applications 67 (2007), no. 8, 2350-2360. (DOI: 10.1016/j.na.2006.08.032)
30. Koji Aoyama and Wataru Takahashi, Weak convergence theorems by Ces\`aro means for a nonexpansive mapping and an equilibrium problem, Pacific Journal of Optimization 3 (2007), no. 3, 501-509.
31. Koji Aoyama, Yasunori Kimura, Wataru Takahashi, and Masashi Toyoda, Finding common fixed points of a countable family of nonexpansive mappings in a Banach space, Scientiae Mathematicae Japonicae 66 (2007), no. 1, 89-99.
32. Koji Aoyama, Hideaki Iiduka, and Wataru Takahashi, Strong convergence of Halpern's sequence for accretive operators in a Banach space, Panamerican Mathematical Journal 17 (2007), no. 3, 75-89.
33. Koji Aoyama, Hideaki Iiduka, and Wataru Takahashi, Weak convergence of an iterative sequence for accretive operators in Banach spaces, Fixed Point Theory and Applications (2006), Art. ID 35390, 13.
34. Koji Aoyama, Inverse of the Berge maximum theorem in convex metric spaces , Scientiae Mathematicae Japonicae 58 (2003), no. 3, 541-546.

# Proceedings

1. Koji Aoyama, Approximation of fixed points of nonexpansive mappings and quasinonexpansive mappings in a Hilbert space, in Proceedings of the 10th International Conference on Nonlinear Analysis and Convex Analysis, Yokohama Publishers, 2019, pp. 1-10.
2. Koji Aoyama, Strongly quasinonexpansive mappings, in Proceedings of the 9th International Conference on Nonlinear Analysis and Convex Analysis, Yokohama Publishers, 2016, pp. 19-27.
3. Koji Aoyama, Approximations to solutions of the variational inequality problem for inverse-strongly-monotone mappings, in Proceedings of 7th international conference on Nonlinear Analysis and Convex Analysis -I-, Yokohama Publishers, 2013, pp. 1-9.
4. Koji Aoyama and Yasunori Kimura, A note on the hybrid steepest descent methods, in Proceedings of The 10th International Conference on Fixed Point Theory and its Applications, House of the Book of Science, Cluj-Napoca, Romania, 2013, pp. 73-80.
5. Koji Aoyama, Asymptotic fixed points of sequences of quasi-nonexpansive type mappings, in Proceedings of the International Symposium on Banach and Function Spaces III, Yokohama Publishers, 2011, pp. 343-350. Comment
6. Koji Aoyama, Halpern's iteration for a sequence of quasinonexpansive type mappings, in Nonlinear Mathematics for Uncertainty and Its Applications (Advances in Intelligent and Soft Computing), Springer-Verlag, 2011, pp. 387-394. PDF
7. Koji Aoyama, An iterative method for a variational inequality problem over the common fixed point set of nonexpansive mappings, Proceedings of the 6th International Conference on Nonlinear Analysis and Convex Analysis, Yokohama Publishers, 2010, pp. 21-28.
8. Koji Aoyama, An iterative method for fixed point problems for sequences of nonexpansive mappings, Proceedings of The 9th International Conference on Fixed Point Theory and its Applications, Yokohama Publishers, 2010, pp. 1-7.
9. Koji Aoyama, Fumiaki Kohsaka, and Wataru Takahashi, Strong convergence theorems for a family of mappings of type (P) and applications, Proceedings of Asian Conference on Nonlinear Analysis and Optimization, Yokohama Publishers, 2009, pp.1-17.
10. Koji Aoyama, Fumiaki Kohsaka, and Wataru Takahashi, Strong convergence theorems by shrinking and hybrid projection methods for relatively nonexpansive mappings in Banach spaces, Proceedings of the 5th International Conference on Nonlinear Analysis and Convex Analysis, Yokohama Publishers, 2009, pp. 7-26.
11. Koji Aoyama, Yasunori Kimura, Wataru Takahashi, and Masashi Toyoda, Strongly nonexpansive sequences and their applications in Banach spaces, Proceedings of the 8th International Conference on Fixed Point Theory and Its Applications, Yokohama Publishers, 2008, pp. 1-18.
12. Koji Aoyama, Kazutaka Eshita, and Wataru Takahashi, Iteration processes for nonexpansive mappings in convex metric spaces, Proceedings of the 4th International Conference on Nonlinear Analysis and Convex Analysis, Yokohama Publishers, 2007, pp. 31-39.
13. Koji Aoyama, A survey: An inverse of the Berge maximum theorem, Proceedings of the 3rd International Conference on Nonlinear Analysis and Convex Analysis, Yokohama Publishers, 2004, pp. 1-8.

# Preprints

• Koji Aoyama and Masashi Toyoda, Mean convergence theorems with respect to attractive points in a Hilbert space, arXiv:2205.11045 [math.FA].
• Koji Aoyama, A quasinonexpansive extension of a mapping with an attractive point in a Hilbert space, arXiv:2202.01419 [math.FA].
• Koji Aoyama and Masashi Toyoda, Fixed point theorem for a Meir-Keeler type mapping in a metric space with a transitive relation, arXiv:2012.14121 [math.FA].
• Koji Aoyama and Masashi Toyoda, Approximation of common fixed points of strongly nonexpansive sequences in a Banach space, arXiv:1804.10757 [math.FA] .
• Koji Aoyama, Approximation of fixed points of nonexpansive mappings and quasinonexpansive mappings in a Hilbert space, arXiv:1709.08901 [math.FA] .
• Koji Aoyama and Kei Zembayashi, Strongly quasinonexpansive mappings, II, arXiv:1703.02218 [math.FA].
• Koji Aoyama, Yasunori Kimura, and Fumiaki Kohsaka, Strong convergence theorems for strongly relatively nonexpansive sequences and applications, arXiv:1202.1628 [math.FA].
• Koji Aoyama and Yasunori Kimura, A note on the hybrid steepest descent methods, arXiv:1101.0881 [math.FA].

# Oral Presentations

1. Koji Aoyama, Approximation of common fixed points of a sequence of nonexpansive mappings, Workshop on Convex Analysis and Optimization, Tokai University, Kanagawa, Japan, December 24, 2019.
2. Koji Aoyama, Approximation of zeros of accretive operators in a Banach space, The 10th international conference on Nonlinear Analysis and Convex Analysis,
Chitose City Cultural Center Hokkaido, Chitose, Japan, July 4-9, 2017.
3. Koji Aoyama, Uniformly nonexpansive sequences, The fifth Asian conference on Nonlinear Analysis and Optimization,
Toki Messe Niigata Convention Center, Niigata, Japan, August 1-6, 2016.
4. Koji Aoyama, Approximation method for the variational inequality problems over the fixed point sets of quasinonexpansive mappings, The ninth international conference on Nonlinear Analysis and Convex Analysis,
Rimkok Resort Hotel, Chiang Rai, January 21-25, 2015.
5. Koji Aoyama, Viscosity approximation process for a sequence of quasinonexpansive mappings, The Fourth Asian Conference on Nonlinear Analysis and Optimization,
National Taiwan Normal University, Taipei, Taiwan, August 5-9, 2014.
6. Koji Aoyama, Viscosity approximation methods with a sequence of contractions, International Conference on Nonlinear Analysis and Optimization,
National Sun Yat-sen University, Kaohsiung, Taiwan, December 20-22, 2013.
7. Koji Aoyama, Strong convergence theorems for strongly relatively nonexpansive sequences and applications, The eighth international conference on Nonlinear Analysis and Convex Analysis,
Hirosaki University, Hirosaki, Aomori, JAPAN on August 2-6, 2013.
8. Koji Aoyama, Existence of fixed points of firmly nonexpansive-like mappings in Banach spaces, International Conference on the Theory, Methods and Applications of Nonlinear Equations, Texas A&M University-Kingsville, Kingsville, Texas, USA, December 17-21, 2012.
9. Koji Aoyama, Strong convergence theorems for strongly nonexpansive sequences in Hilbert spaces, The Third Asian Conference on Nonlinear Analysis and Optimization, Kunibiki Messe, Matsue, Shimane, Japan, September 2-6, 2012.
10. Koji Aoyama, Fixed point and mean convergence theorems for hybrid mappings, The 10th International Conference on Fixed Point Theory and its Applications, Babes-Bolyai University, Cluj-Napoca, Romania, July 9-15, 2012.
11. Koji Aoyama, Halpern's iteration for a sequence of quasinonexpansive type mappings, International Conference on Nonlinear Mathematics for Uncertainty and Its Applications, Beijing University of Technology, Beijing, China, September 7-9, 2011.
12. Koji Aoyama, On the hybrid steepest descent method, The 7th International Conference on Nonlinear Analysis and Convex Analysis, Pukyong National University, Busan, Republic of Korea, August 2-5, 2011.
13. Koji Aoyama, Convergence theorems for relatively nonexpansive mappings in Banach spaces, The Second Asian Conference on Nonlinear Analysis and Optimization, Royal Paradise Hotel & Spa, Patong beach, Phuket, Thailand, September 9-12, 2010.
14. Koji Aoyama, Approximation methods for a countable family of nonexpansive mappings, The Third International Symposium on Banach and Function Spaces, Kyushu Institute of Technology, Tobata Campus, Kitakyushu, Japan, September 14-17, 2009.
15. Koji Aoyama, On a strongly nonexpansive sequence in Banach spaces, The Ninth International Conference on Fixed Point Theory and Its Applications, National Changhua University of Education, Changhua, Taiwan, July 16-22, 2009.
16. Koji Aoyama, Maximal monotone operators and equilibrium problems, The Sixth International Conference on Nonlinear Analysis and Convex Analysis, Tokyo Institute of Technology, Tokyo, Japan, March 27-31, 2009.
17. Koji Aoyama, Strongly nonexpansive sequences and their applications, Asian Conference on Nonlinear Analysis and Optimization, Kunibiki Messe, Matsue, Japan, September 14-17, 2008.
18. Koji Aoyama, Strongly nonexpansive sequences and their applications, The Fifth World Congress of Nonlinear Analysts, Hyatt Grand Cypress Resort, Orlando, Florida, USA, July 2-9, 2008.
19. Koji Aoyama and Wataru Takahashi, Convergence theorems for a nonexpansive mapping and an equilibrium problem in Hilbert spaces, The Japan-Thailand joint seminar on fixed point algorithms in optimization, Tokyo Institute of Technology, Tokyo, Japan, September 6-7, 2007.
20. Koji Aoyama, Yasunori Kimura, Wataru Takahashi and Masashi Toyoda, Approximation of common fixed points of a family of nonexpansive mappings in a Banach space, The eighth international conference on fixed point theory and its applications, Chiang Mai University, Chiang Mai, Thailand, July 16-22, 2007.
21. Koji Aoyama and Wataru Takahashi, Strong convergence theorems for a family of relatively nonexpansive mappings in Banach spaces, The fifth international conference on nonlinear analysis and convex analysis, National Tsing-Hua University, Hsinchu, Taiwan, May 30-June 4, 2007.
22. Koji Aoyama, A sufficient condition for Nash equilibria in $N$-person games over reflexive Banach spaces, The fourth international conference on nonlinear analysis and convex analysis, Okinawa Convention Center, Okinawa, Japan, June 30-July 4, 2005.
23. Koji Aoyama, An inverse of the Berge maximum theorem, The eighth international conference on nonlinear functional analysis and applications, Kyungnam University and Gyeongsang National University, Masan and Chinju, Korea, August 9-13, 2004.
24. Koji Aoyama, Inverse of the Berge maximum theorem in convex metric spaces, The third international conference on nonlinear analysis and convex analysis, Tokyo Institute of Technology, Tokyo, Japan, August 25-29, 2003.