By Anastassiou G.A. (ed.)

In October 1998 a convention was once held in Lisbon to have a good time the sixtieth birthday of Ludwig Streit. This quantity collects a number of the papers awarded on the convention in addition to different essays contributed via the numerous acquaintances and collaborators who desired to honour Ludwig Streit's medical profession and character. The individuals conceal many facets of latest mathematical physics. Of specific significance have been new effects on infinite-dimensional stochastic research and its purposes to a variety of actual domain names modern computational recommendations in numerical research, I.K. Argyros; at the simultaneous approximation of services and their derivatives, T. Kilgore; copositive polynomial approximation revisited, Y.K. Hu and M. Yu; sampling thought and serve as areas, H-J. Schmeisser and W. Sickel; comparing statistical functionals via projections onto convex cones in Hilbert areas - half I and II, T. Rychlik; extrapolation - from calculation of pie to finite aspect approach to partial differential equations, X-P. Shen; a survey on scaling functionality interpolation and approximation, E-B. Lin. (Part contents)

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**Example text**

47) We also have F"{y' + t(y0 - j/')](l - t)(y0 - y*)2dt, F(yo) - F(y*) - F'(y-)(y0 - y') = f Jo which together with (38), (39), find (41) give + a\\yo - y (2 + 7)(3 + 7)m! \\F(yo)\\ = \\F(yo)-F(y')\\

47 Example 1. A classical example of modular space is the Orlicz space gener ated by a ip-function ip (see [29], [25]). The corresponding modular is defined by: P(f) = Iv(f) ■■■ /

C3, C4, C5, C6 with C4 > P3 and an integer /ii > 0 such that for 0 < po < C4 - c5<5h < r 0 (/i) = r(/i) < c36,, < P l < r 0 < R (67) and r(/i) = 0 when ao = a* or h = 00, the following are true for sufficiently small r0,R > 0 and h> hi 0 < <52 < tfi(r(h)) < p 3 and 0(r{h)) < 1, (68) where 0{r) = C{R,r,r + R) -\ C2{R,r) + C3{R,r,r + R) + 62 +64 (69) provided that b\ + b4 £ [0,1). We can now show that for all h > /14, where /i4 = max{/ii,/i2,/i3} where c 3 > C6,C6 > c2 and /i 2 , /13 are integers such that , , c4 - <^3 .