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  • [ X ]
    Öğe
    Esnek limit ve esnek süreklilik üzerine
    (Çanakkale Onsekiz Mart Üniversitesi, 2018) Sapan, Kenan; Enginoğlu, Serdar
    Esnek kümeler teorisi, belirsizlikle başa çıkabilmek için Molodtsov (1999) tarafından ortaya atıldı. Daha sonra, cebirden karar verme problemlerine kadar pek çok alana uygulandı. Bu çalışmada, ilk olarak, bazı temel kavramlar verildi. Ardından, esnek limit ve esnek süreklilik kavramları (Molodtsov, 1999, 2004) ve bazı temel özelikleri incelendi. Daha sonra, bu kavramlar klasik anlamda limit ve süreklilikle karşılaştırıldı. Son olarak sonraki çalışmalar hakkında bir tartışmaya yer verildi.
  • [ X ]
    Öğe
    Soft Limit and Soft Continuity
    (Mdpi, 2025) Sapan, Kenan; Arslan, Burak; Enginoglu, Serdar
    This study presents the soft limit and upper (lower) soft limit proposed by Molodtsov, with several theoretical contributions. It investigates some of their basic properties, such as some fundamental soft limit rules, the relation between soft limit and boundedness, and the sandwich/squeeze theorem. Moreover, the paper proposes left and right soft limits and studies some of their main properties. Furthermore, it defines the soft limit at infinity and explores some of its basic properties. Additionally, the present study exemplifies these concepts and their properties to better understand them. The paper then compares the aforesaid concepts with their classical forms. Afterward, this paper presents soft continuity and upper (lower) soft continuity, proposed by Molodtsov, theoretically contributes to these concepts, and investigates some of their key properties, such as some fundamental soft continuity rules, the relation between soft continuity and boundedness, Bolzano's theorem, and the intermediate value theorem. Moreover, it defines left and right soft continuity and studies some of their basic properties. The present study exemplifies soft continuity types and their properties. In addition, it compares them with their classical forms. Finally, this study discusses whether the aspects should be further analyzed.