1. R. E. Lane, Absolute convergence of continued fractions, Proc. Amer. Math. Soc. vol. 3 (1952) pp. 904-913. 2. R. E. Lane and H. S. Wall, Continued fractions with absolutely convergent even and odd parts, Trans. Amer. Math. Soc. vol. 67 (1949) pp. 368-380. 3. W. T. Scott and H. S. Wall, A convergence theorem for continued fractions, Trans. Amer. Math. Soc. vol. 47 (1940) pp. 155-172. 4. H. S....

Inclusion relations for k−uniformly starlike functions under the Dziok-Srivastava operator are established. These results are also extended to k−uniformly convex functions, close-to-convex, and quasi-convex functions.

We construct a quasi-Banach space which cannot be given an equivalent plurisubharmonic quasi-norm, but such that it has a quotient by a onedimensional space which is a Banach space. We then use this example to construct a compact convex set in a quasi-Banach space which cannot be atfinely embedded into the space L0 of all measurable functions.

A parametric version of the Borwein-Preiss smooth variational principle is presented, which states that under suitable assumptions on a given convex function depending on a parameter, the minimum point of a smooth convex perturbation of it depends continuously on the parameter. Some applications are given: existence of a Nash equilibrium and a solution of a variational inequality for a system o...

The Schatten quasi-norm was introduced tobridge the gap between the trace norm andrank function. However, existing algorithmsare too slow or even impractical for large-scale problems. Motivated by the equivalencerelation between the trace norm and its bilin-ear spectral penalty, we define two tractableSchatten norms, i.e. the bi-trace and tri-tracenorms, and prov...