Paper's Title:

Some Properties of Cosine Series with Coefficients from Class of General Monotone Sequences Order r

Author(s):

Corina Karim, Moch. Aruman Imron

Department of Mathematics,
Universitas Brawijaya,
Indonesia.
E-mail: co_mathub@ub.ac.id
maimr@ub.ac.id

Abstract:

The coefficient of sine series from general monotone class has been generalized by Bogdan Szal to the new class which is called class of general monotone order r. This coefficient class is more general than class of general monotone introduced by Tikhonov. By special case, we study properties of cosine series with coefficient of sine series from the class of general monotone order r.

Paper's Title:

Stability of an Almost Surjective epsilon-Isometry in The Dual of Real Banach Spaces

Author(s):

Minanur Rohman, Ratno Bagus Edy Wibowo, Marjono

Department of Mathematics, Faculty of Mathematics and Natural Sciences,
Brawijaya University,
Jl. Veteran Malang 65145,
Indonesia.
E-mail: miminanira@gmail.com

Department of Mathematics, Faculty of Mathematics and Natural Sciences,
Brawijaya University,
Jl. Veteran Malang 65145,
Indonesia.
E-mail: rbagus@ub.ac.id

Department of Mathematics, Faculty of Mathematics and Natural Sciences,
Brawijaya University,
Jl. Veteran Malang 65145,
Indonesia.
E-mail: marjono@ub.ac.id

Abstract:

In this paper, we study the stability of epsilon-isometry in the dual of real Banach spaces. We prove that the almost surjective epsilon-isometry mapping is stable in dual of each spaces. The proof uses Gâteaux differentiability space (GDS), weak-star exposed points, norm-attaining operator, and some studies about epsilon-isometry that have been done before.