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4: Paper Source PDF document

Paper's Title:

The Concept of Convergence for 2-Dimensional Subspaces Sequence in Normed Spaces


M. Manuharawati, D. N. Yunianti, M. Jakfar

Mathematics Department, Universitas Negeri Surabaya,
Jalan Ketintang Gedung C8,
Surabaya 60321,


In this paper, we present a concept of convergence of sequence, especially, of 2-dimensional subspaces of normed spaces. The properties of the concept are established. As consequences of our definition in an inner product space, we also obtain the continuity property of the angle between two 2-dimensional subspaces of inner product spaces.

2: Paper Source PDF document

Paper's Title:

New Refinements for Integral and Sum Forms of Generalized Hölder Inequality For N Term


M. Jakfar, Manuharawati, D. Savitri

Mathematics Department,
Universitas Negeri Surabaya
Jalan Ketintang Gedung C8, Surabaya, 60321


We know that in the field of functional analysis, Hölder inequality is very well known, important, and very applicable. So many researchers are interested in discussing these inequalities. Many world mathematicians try to improve these inequalities. In general, the Hölder inequality has two forms, namely the integral form and the sum form. In this paper, we will introduce a new refinement of the generalization of Hölder inequalities in both integral and addition forms. Especially in the sum form, improvements will be introduced that are better than the previous improvements that have been published by Jing-feng Tian, Ming-hu Ha, and Chao Wang.

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