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RETRACTED At the request of the authors, this article has been retracted. The article was found by the authors to contain a number of mathematical errors, undefined expressions, and spelling errors, which mean that the conclusions cannot be relied upon.

International Journal of Analysis - Volume 2014 2014, Article ID 258389, 7 pages -

Research Article

Department of Mathematics, Batman University, 72100 Batman, Turkey

Department of Mathematics, Inonu University, 44280 Malatya, Turkey

Received 25 November 2013; Revised 17 January 2014; Accepted 23 January 2014; Published 11 March 2014

Academic Editor: Malte Braack

Copyright © 2014 Hacer Bozkurt et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Aseev launched a new branch of functional analysis by introducing the theory of quasilinear spaces in the framework of the topics of norm, bounded quasilinear operators and functionals Aseev 1986. Furthermore, some quasilinear counterparts of classical nonlinear analysis that lead to such result as Frechet derivative and its applications were examined deal with. This pioneering work causes a lot of results in such applications such as Rojas-Medar et al. 2005, Talo and Başar 2010, and Nikol'skiĭ 1993. His work has motivated us to introduce the concept of quasilinear inner product spaces. Thanks to this new notion, we obtain some new theorems and definitions which are quasilinear counterparts of fundamental definitions and theorems in linear functional analysis. We claim that some new results related to this concept provide an important contribution to the improvement of quasilinear functional analysis.

Autor: Hacer Bozkurt, Sümeyye Çakan, and Yılmaz Yılmaz

Fuente: https://www.hindawi.com/


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