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On stability of index of Fredholm complexes on the C^*-algebra
S. Bayramov 장전수학회 2006 Proceedings of the Jangjeon mathematical society Vol.9 No.2
This paper deals with the index of Fredholm complexes of ¤-operators of the Hilbert ¤-modulus on C¤- algebra. For these class of operators a necessary and su±cient conditions in order to be a Fredholm, are obtained. Based on these results a notion of Fredholm complex and its index is introduced. For this index a stability theorem related to various perturbations is proved. In the second part of the paper a completation of a semigroup Fredholm complexes is analysed. It is proved that the group KG(X; ¤) is the completation of G ¡ ¤-¯bration of the above group on the compact space X.
THE REGULARIZED TRACE FORMULA FOR A DIFFERENTIAL OPERATOR WITH UNBOUNDED OPERATOR COEFFICIENT
E. Şen,A. Bayramov,K. Oruçoğlu 장전수학회 2015 Advanced Studies in Contemporary Mathematics Vol.25 No.4
In this paper, rstly we investigated the spectrum and resolvent operator of a Sturm-Liouville type di¤erential operator. Finally we have obtained the regularized trace formula for di¤erential operator equation with unbounded operator coe¢ cient.
Compactness in soft $S$-metric spaces
Cigdem Gunduz Aras,Sadi Bayramov,Vefa Cafarli 원광대학교 기초자연과학연구소 2020 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.20 No.1
The first aim of this paper is to contribute for investigating on soft $S-$ metric space which is based on soft points of soft sets and to prove some important theorems on sequential compact and totally bounded in soft $S-$ metric space. Moreover, we introduce soft uniformly continuous mapping and examine some of its properties.
Algebraic structures on fuzzy homotopy sets
C. Gunduz,S. Bayramov 장전수학회 2006 Proceedings of the Jangjeon mathematical society Vol.9 No.2
In this paper, firstly, the concepts of fuzzy compactness , fuzzy Hausdorff and fuzzy locally compact are defined. Using these concepts, fuzzy compact-open topology is given on fuzzy function spaces. Further, function spaces are defined and some properties of the function spaces are investigated. Secondly, fuzzy H − space and fuzzy H − cospace are defined.
A Note on Bipolar Soft Supra Topological Spaces
ÇIĞDEM GÜNDÜZ ARAS,Sadi Bayramov,ARZU ERDEM COŞKUN 한국수학교육학회 2023 純粹 및 應用數學 Vol.30 No.4
In this paper, we present bipolar soft supra topological space and characterize the concepts of bipolar soft supra closure and bipolar soft supra interior. We connect bipolar soft supra topology and bipolar soft topology. We intoduce the concepts of bipolar soft supra continuous mapping and study the concept of bipolar soft supra compact topological space. We prove a result related to the image of the bipolar soft supra compact space. We identify the concepts of disconnected (connected) and strongly disconnected (strongly connected) space and obtain several results connecting among them herein. We clarify the relationships among these concepts by examples.
Some notes on compact sets in soft metric spaces
Cigdem Gunduz Aras,Murat Ibrahim Yazar,Sadi Bayramov 원광대학교 기초자연과학연구소 2017 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.14 No.4
The first aim of this study is to define soft sequential compact metric spaces and to investigate some important theorems on soft sequential compact metric space. Second is to introduce $\tilde{\varepsilon}-$net and totally bounded soft metric space and study properties of this space. Third is to define Lebesque number for soft sets and soft uniformly continuous mapping and investigate some theorems in detail.
Cigdem Gunduz Aras,Taha Yasin Ozturk,Sadi Bayramov 원광대학교 기초자연과학연구소 2017 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.13 No.5
Soft topological spaces based on soft set theory which is a new mathematical tool for dealing with uncertainties. In this paper, the notions of $% \widetilde{I}_{\noindent \widetilde{c}}$ soft free ideal and soft $\widetilde{% c}-$ ideals are introduced. Also, soft ideal extension of a given soft topological space is investigated via the concept of soft ideals.