Seminar on Nonlinear Analysis

Mini-workshop on nonlinear analysis

May 14, 2025

Date/Time

Wednesday, May 14, 2025 / 10:30am (tentative)

Venue

Room 4430, Building IV
Toho University Narashino Campus (Google Map)

Session (tentative)

1. Professor Kunquan Lan (Toronto Metropolitan University, Canada), An introduction to fractional derivatives, fractional integrals and fractional differential equations.

   ABSTRACT: In this presentation, I'll discuss the definitions and properties of fractional integrals, fractional derivatives and nonlinear first order fractional differential equations based on my recent study on fractional calculus, see the list of papers below. There are so many wrong papers on fractional calculus in the literature, so working on a correct framework of fractional calculus is of importance to research.

   1. K. Q. Lan, Equivalence of higher order linear Riemann-Liouville fractional differential and integral equations, Proc. Amer. Math. Soc. 148 (2020) (12), 5225-5234.
   2. K. Q. Lan, Linear first order Riemann-Liouville fractional differential and perturbed Abel's integral equations, J. Differential Equations, 306 (2022), 28 59.
   3. K. Q. Lan, Linear higher-order fractional differential and integral equations, Electr. J. Differ. Equ. (2023), No. 01, pp. 1-20.
   4. K. Q. Lan, Existence and uniqueness of solutions of nonlinear Cauchy-type problems for first-order fractional differential equations, Math. Meth. Appl. Sci., 47 (2024) (1), 535-555.
   5. K. Q. Lan, Generalizations of Riemann-Liouville fractional integrals and applications, Math. Meth. Appl. Sci. 47 (2024) (16), 12833-12870.
   6. K. Q. Lan, Existence and uniqueness of generalized normal solutions to first order fractional differential equations and applications, Electr. J. Differ. Equ. (2024), No. 81, pp. 1-16.
   7. K. Q. Lan, Initial value problems of first order fractional differential equations via monotone iterative techniques, Discrete Contin. Dyn. Syst. Ser ies S, (2024). DOI: 10.3934/dcdss.2024169,
   8. K. Q. Lan, A basic theory for initial value problems of first order ordinary differential equations with $L^{p}$-Carath\'{e}odory functions and applications, J. Differential Equations, 386 (2024), 368-403.
   9. Kunquan Lan, Equivalences of nonlinear higher order fractional differential e quations with integral equations, Math. Meth. Appl. Sci. 48 (2025) (6), 6930-6942.
   10. K. Q. Lan and J. R. L. Webb, A new Bihari inequality and initial value problems of first order fractional differential equations, Fract. Calc. Appl. Anal. 26 (2023), 962-988.

   Some of the above papers can be downloaded from my website: https://math.ryerson.ca/~klan/Publications.html

Mini-workshop on convex analysis and optimization for young scholars

December 6, 2024

Date/Time

Friday, December 6, 2024 / 3:00pm-

Venue

Room 4430, Building IV
Toho University Narashino Campus (Google Map)

Student session

1. Shuta Sudo (Toho University, Japan), Convexity of half spaces on a Hadamard space

   ABSTRACT: In this talk, we deal with convexity of two sorts of half spaces on a Hadamard space. We will use a notion of tangent spaces on a Hadamard space to define a half space. (extended abstract)

2. Takuto Kajimura (Toho University, Japan), A vicinal mapping in geodesic spaces and their properties

   ABSTRACT: In this talk, we introduce the class of vicinal mappings on geodesic spaces and show their fundamental properties.

Regular session

1. Dr. Kazuya Sasaki (Toho University, Japan), A convex combination and the Nakajo-Takahashi projection method on hyperbolic spaces

   ABSTRACT: In this talk, we consider two types of convex combinations on a hyperbolic space. We also investigate convexity of some half spaces related to the Nakajo-Takahashi projection method in a hyperbolic space.

2. Professor Wei-Shih Du (National Kaohsiung Normal University, Taiwan), New integral inequalities and generalizations with their applications.

   ABSTRACT: In this talk, we first establish some new integral inequalities. As applications, some generalizations and new inequalities for exponential functions, hyperbolic functions and other functions are also given.

Special Lecture on Nonlinear Analysis

June 7, 2024

Date/Time

Friday, June 7, 2024 / 4:00pm-

Venue

Room 4430, Building IV
Toho University Narashino Campus (Google Map)

Speaker

Professor Supaluk Phothi (Chiang Mai University, Thailand)

Title

Measures of non-compactness in modular spaces and some fixed point theorems (Abstract)