2021

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PREFACE

academic society through editorial activities in international journals. He is one of
the founding editors of the Journal of Nonlinear and Convex Analysis, founded in
2000, the leading journal in this ﬁeld. His name is on the list of the editorial boardof various journals.
He was also one of the prominent founding members of two conference series:
International Conference on Nonlinear Analysis and Convex Analysis (NACA) andAsian conference on Nonlinear Analysis and Optimization (NAO-Asia). The latest
11th NACA conference took place in Hakodate, Hokkaido, Japan, on August 2019,as the celebrated joint conference with the International Conference on Optimization: Techniques and Applications (ICOTA). At this conference, they held a special
celebrating session for Professor Wataru Takahashi on his 75th birthday.
Professor Takahashi was also a successful educator. “Forty-three students
obtained their Ph.D. degrees under his supervision”. Most of them are
active research mathematicians in their academic ﬁeld.
He created an international network of researchers that brought together people
from many countries and provided them new ways to communicate and publish
their work. The following messages from his friends tell a lot about his character.
“The passing of Wataru Takahashi is a huge loss to the mathematical world.
Beyond his numerous academic contributions, he created an international networkof researchers that brought together people from many countries and provided them
new ways to communicate and publish their work. The cycles of meetings he started
up have been a scientiﬁc beneﬁt and source of yearly travel pleasure for very manyof us, and for me particularly. Without them and his kind invitations, I would nothave learned to know so many colleagues in Asia and to love so much the cultureof Japan and its neighbors. I will greatly miss him and his inﬂuential eﬀorts.”——Terry Rockafellar“It was 1999, that I wrote the ﬁrst letter to Professor Takahashi and asked him
for suggestions on the struggling in my research, and he kindly introduced me thebook written by him. The book and many others books under his name are very
helpful to my works, thereafter. Years after our ﬁrst contact, he made the ﬁrst visit
to my university, Chulalongkorn University in Bangkok, gave lecture to participantsfrom many universities in the country. Since then, many Thai PhD students had
worked under his supervision. As a very kind teacher and a beloved friend he will
be in my heart forever.”——Imchit Termwuttipong“Wataru had been an Honorary Chair Professor of our Department of Applied
Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan, for about 10years. Among his 524 publications found in Mathscinet, there are 17 papers coauthored with me, 70 papers addressed to our department, and about 200 papers
joined with colleagues in Taiwan. It is never overemphasized how important thecontribution Wataru made to the ﬁeld of analysis in Taiwan. We are in deep sorrow

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in the loss of our best friend, best colleague, and best teacher, Wataru Takahashi
Sensei. May Sensei rest in peace.”——Ngai-Ching Wong
“ Professor Wataru Takahashi has been known to me for a long time as an expert ofnonlinear and convex analysis, and I actually had occasional email correspondenceswith him for many years, but it was only recently that I had the chance to talkto him personally. In 2018 I was invited to give a talk at the 6th conference ofNAO-Asia in Okinawa on some work on discrete optimization related to convexity.
In NAO-Asia 2018, it was impressive for me to witness an international community of nonlinear analysis that Professor Takahashi developed with enthusiasm andfriendship. Not only elderly established researchers but younger people also enjoyed
the friendly conference with substantial scientiﬁc interaction. On top of his numerous mathematical papers and books, his contribution to forming an international
community, especially in Asia, is outstanding. I am really sorry for the loss of suchan international leader, and I can only hope that his enthusiasm will be inheritedby his successors.”——Kazuo Murota
Full text and other messages can be found in:
https://www.lab2.toho-u.ac.jp/sci/is/kimura/en/takahashi-memorial.html

We feel that this special issue will be of great importance for many mathematicians and scientists, who are interested in recent developments in nonlinear andconvex analysis as well as in their numerous applications.

Editors