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Öğe AN APPROACH TO THE CONCEPT OF SOFT VIETORIS TOPOLOGY(Etamaths Publ, 2016) Demir, İzzettinIn the present paper, we study the Vietoris topology in the context of soft set. Firstly, we investigate some aspects of first countability in the soft Vietoris topology. Then, we obtain some properties about its second countability.Öğe COMMON FIXED SOFT ELEMENT RESULTS IN SOFT COMPLEX VALUED b-METRIC SPACES(Turkic World Mathematical Soc, 2021) Demir, İzzettinIn this paper, firstly, on the base of the soft complex numbers suggested by Das and Samanta, we introduce the concept of a soft complex valued b-metric space and investigate some of its properties. Also, we compare it to a soft complex valued metric space and a soft topological space. Next, we establish some fixed soft element theorems in the context of soft complex valued b-metric spaces and give suitable examples to illustrate the usability of the obtained main results. These results extend and generalize the corresponding results given in the existing literature.Öğe A Contribution to the Study of Soft Proximity Spaces(Univ Nis, Fac Sci Math, 2017) Demir, İzzettin; Özbakır, Oya Bedre; Yıldız, İsmetIn this paper we study the soft proximity spaces. First, we investigate the relation between proximity spaces and soft proximity spaces. Also, we define the notion of a soft delta-neighborhood in the soft proximity spaces which offer an alternative approach to the study of soft proximity spaces. Later, we show how a soft proximity space is derived from a soft uniform space. Finally, we obtain the initial soft proximity space determined by a family of soft proximity spaces.Öğe Esnek ve bulanık esnek kümelerin düzgün ve yakınlık uzaylarına uygulanması(Düzce Üniversitesi, 2016) Demir, İzzettin; Yıldız, İsmet; Özbakır, Oya BedreBu tez çalışmasında, öncelikle esnek küme teorisi kullanılarak esnek düzgün uzaylar tanımlanmış ve bu uzaylar yardımıyla bir esnek topolojik uzay elde edilmiştir. Esnek yakınlık uzaylarıyla ilgili özellikler incelenmiş ve esnek düzgün uzaylar ile ilişkisi araştırılmıştır. Sabit nokta teorisi üzerinde çalışabilmek için esnek elemanlar yardımıyla bir se-düzgün uzay kavramı tanımlanmıştır. Daha sonra bu uzay üzerinde sabit esnek eleman teoremleri elde edilmiştir. Ayrıca bir bulanık esnek komşuluk sistemi kavramı verilmiş ve özellikleri incelenmiştir. Bunun yanı sıra Lowen anlamında bir bulanık esnek düzgün uzay tanımlanarak bulanık esnek topoloji ve bulanık esnek komşuluk sistemi ile ilişkisi araştırılmıştır. Son olarak bulanık esnek yakınlık uzaylarıyla ilgili özellikler incelenerek klasik anlamdaki yakınlık uzaylarıyla ilişkisi elde edilmiştir.Öğe FIXED POINT THEOREMS IN COMPLEX VALUED FUZZY b-METRIC SPACES WITH APPLICATION TO INTEGRAL EQUATIONS(Univ Miskolc Inst Math, 2021) Demir, İzzettinIn this paper, firstly, we introduce the concept of a complex valued fuzzy b-metric space, which is inspired by the work of Shukla et al. [24]. Also, we investigate some of its topological properties which strengthen this concept. Next, we establish some fixed point theorems in the context of complex valued fuzzy b-metric spaces and give suitable examples to illustrate the usability of the obtained main results. These results extend and generalize the corresponding results given in the existing literature. Moreover, we provide some applications on the existence and uniqueness of solutions for a certain type of nonlinear integral equations.Öğe N-soft mappings with application in medical diagnosis(Wiley, 2021) Demir, İzzettinFatimah et al. suggested different complement operations for N-soft sets. However, these operations do not comply with De Morgan's laws and double complementation law for N-soft sets. So we do not restate some classical theorems on topological spaces in the realm of N-soft sets. Besides, the mappings are a basic mathematical tool which is utilized in numerous areas of mathematics, other sciences, and their applications. But there is not any note on the mappings in the setting of N-soft set theory. To deal with these problems, firstly, we advance the concept of complement of an N-soft set and demonstrate that De Morgan's laws and double complementation law are satisfied in N-soft set theory according to this new definition. Then we present an idea of the N-soft mappings and investigate some of their properties. Also, we illustrate given properties with examples and counter examples. Finally, using the N-soft mappings, we describe a mathematical system design for diagnosing purpose of the Covid-19 disease.Öğe On fixed soft element theorems in se-uniform spaces(Int Scientific Research Publications, 2016) Demir, İzzettin; Özbakır, Oya Bedre; Yıldız, İsmetFirst we introduce a new structure of uniform spaces, called se-uniform spaces, and provide some of their basic properties. Next, we present the notion of a soft E-distance in se-uniform spaces, which is a soft version of E-distance of Aamri and El Moutawakil [M. Aamri, D. El Moutawakil, Acta Math. Acad. Peadegog. Nyhazi., 20 (2004), 83-91]. Then, by using the soft E-distance, we establish some fixed soft element theorems for various mappings on se-uniform spaces, which are the main results of the paper. This is the first kind of such results in this direction. (C)2016 All rights reserved.Öğe Some fixed soft point theorems on a new soft topology related to a self soft mapping(Forum Editrice Univ Udinese, 2019) Demir, İzzettin; Bozyikıt, ResimeIn the present paper, we introduce a new soft topology related to a self soft mapping and study its some basic properties. Also, we give the notion of a soft orbit and support it with examples. Moreover, we present the notion of a soft b-metric space, which is a soft version of b-metric space of Czerwik [7]. Next, by using these notions, we establish some fixed soft point theorems, which are the main results of our paper.Öğe Some Properties of Fuzzy Soft Proximity Spaces(Hindawi Publishing Corporation, 2015) Demir, İzzettin; Özbakır, OyaWe study the fuzzy soft proximity spaces in Katsaras's sense. First, we show how a fuzzy soft topology is derived from a fuzzy soft proximity. Also, we define the notion of fuzzy soft ?-neighborhood in the fuzzy soft proximity space which offers an alternative approach to the study of fuzzy soft proximity spaces. Later, we obtain the initial fuzzy soft proximity determined by a family of fuzzy soft proximities. Finally, we investigate relationship between fuzzy soft proximities and proximities. © 2015 Izzettin Demir and Oya Bedre Özbakr.Öğe Some soft topological properties and fixed soft element results in soft complex valued metric spaces(2021) Demir, İzzettinIn this paper, first, by using the idea of soft complex numbers as in Das and Samanta [8], we introduce thenotion of soft complex valued metric spaces and investigate some of their topological aspects. Next, we establish somefixed soft element theorems for various soft mappings on soft complex valued metric spaces, which are the main resultsof our paper.Öğe Some types of soft paracompactness via soft ideals(Semnan Univ, 2019) Turanlı, Elif; Demir, İzzettin; Özbakır, Oya BedreIn this paper, we introduce the soft I-paracompact spaces and the soft I-S-paracompact spaces. First, we investigate the relationships between these spaces and soft paracompact spaces. Also, we give some fundamental properties of these spaces. Finally, we prove that soft I-S-paracompact spaces are invariant under perfect mappings.
