# Faculty

## Kazuaki Kitahara

### Major research activity

My major research activity is to study various problems of approximation theory, which is one of the fields of mathematics.

For example Let E be a space of functions which is endowed with a distance d(f, g) between two functions f and g, and let G be a subspace of E. Then, it is one of the principal themes in approximation theory to study the following problems: For any given f of E, find f' of G such that d(f, f') is the minimum distance of the distances d(f, g) for all g of G and estimate the minimum distance. G is called an approximating space and f is said to be the best approximation to f from G. If G is chosen in the manner so that the minimum distance is as small as possible and so that functions in G are easy to handle, then G is a good approximating space.

For example, in C[a, b] (= the space of all real-valued continuous functions on [a, b]) with the uniform norm, i.e., a useful distances between two functions, spaces of polynomials with degree at most n and spaces of continuous and piecewise linear functions with fixed knots are suitable for good approximating spaces to consider best approximations. Chebyshev spaces and weak Chebyshev spaces are generalizations of these two spaces and play a central part when considering the above problems. In fact, properties and characterizations of Chebyshev or weak Chebyshev spaces have been deeply studied since the 20th century. In this situation, I have been studying good generalizations of Chebyshev or weak Chebyshev spaces.

### Major relevant publications

- K. Kitahara and T. Okuno, “A Note on Two Point Taylor Expansion Ⅲ,” International Journal of Modeling and Optimization. 4 (2014), 287 - 291.
- C. Omoto and K. Kitahara, “A visit to the weak elementary Euclidean Pasch free geometry,” Scientiae Mathematicae Japonicae, 76 (2013), 367 - 374.
- K. Kitahara, T. Yamada and K. Fujiwara, “A note on two point Taylor expansion Ⅱ,” International Journal of Pure and Applied Mathematics, 86(2013), 65 - 82.
- K. Kitahara, T. Chiyonobu and H. Tsukamoto, “A note on two point Taylor expansion,” International Journal of Pure and Applied Mathematics, 75(2012), 327 - 338.
- Y. Nishino and K. Kitahara, “Functions approximated by any sequence of interpolating generalized polynomials,” International Journal of Pure and Applied Mathematics, 64(2010), 411 - 420.