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Öğe A paranormed fractional ordered Euler-Riesz difference sequence space(World Scientific Publ Co Pte Ltd, 2024) Bektas, Cigdem A.; Bayram, ErdalIn this study, we introduce a novel sequence space denoted as & ell;((tau))(p) with a fractional order tau. This new space is defined by the matrix B-similar to(Delta((tau))), which is a composition of the Euler-Riesz matrix B-similar to and the fractional ordered difference operator Delta((tau)). We explore its topological properties along with its alpha-, beta-, and gamma-duals. Furthermore, we provide characterizations for certain matrix mappings from & ell;((tau))(p) to the sequence spaces of Maddox.Öğe Banach lattices of L-weakly and M-weakly compact operators(Springer Basel Ag, 2017) Bayram, Erdal; Wickstead, A. W.We give conditions for the linear span of the positive L-weakly compact (resp. M-weakly compact) operators to be a Banach lattice under the regular norm, for that Banach lattice to have an order continuous norm, to be an AL-space or an AM-space.Öğe Invariant subspaces of operators quasi-similar to L-weakly and M-weakly compact operators(Scientific Technical Research Council Turkey-Tubitak, 2018) Bayram, ErdalLet T be an L-weakly compact operator defined on a Banach lattice E without order continuous norm. We prove that the bounded operator S defined on a Banach space X has a nontrivial closed invariant subspace if there exists an operator in the commutant of S that is quasi-similar to T. Additively, some similar and relevant results are extended to a larger classes of operators called super right-commutant. We also show that quasi-similarity need not preserve L-weakly or M-weakly compactness.Öğe L- ve M-zayıf Kompakt Operatörlerin Sıra Yapısı Üzerine(2018) Bayram, ErdalBanach örgüleri üzerinde tanımlı zayıf kompakt operatörlerin alt sınıfları olan L-zayıf ve M-zayıf kompaktoperatörlerin genelde vektör örgüsü olmadıkları bilinmesine rağmen sıra yapılarına dair çalışmalar literatürdegörünmemektedir. Birçok operatör sınıfının aksine baskınlık özelliğine sahip olmalarının bir sonucu olarak, yakınzamanda daha dar bir sınıf olan pozitif L-zayıf ve pozitif M-zayıf kompakt operatörlerin ürettiği sınıfların, sırayapılarına ilişkin sahip oldukları önemli özellikler verilmiştir [3]. Sunulan çalışmada da bu sonuçların bir devamıniteliğinde olan, söz konusu operatör sınıflarının regüler operatörler sınıfı içinde band ve KB-uzay olmakoşullarına dair bazı sonuçlar verilmiştir. Ayrıca L-zayıf veya M-zayıf kompakt operatörler, regüler olanları vepozitif olanları ile üretilmiş sınıfların çakıştıkları durumlar da irdelenmiştiÖğe L-weakly and M-weakly compact operators and the centre(Springer Basel Ag, 2017) Bayram, Erdal; Wickstead, A. W.We extend known results concerning the centre of spaces of regular (resp. weakly compact or compact) operators between two Banach lattices to the setting of L-weakly compact and M-weakly compact operators. We also show that the L-weakly compact, M-weakly compact, and compact operators lying in the centre of a Banach lattice coincide.Öğe LACUNARY STATISTICAL CONVERGENCE OF ORDER ? IN PARTIAL METRIC SPACES(Univ Nis, 2023) Bayram, Erdal; Bektas, Cigdem A.The present study introduces the notions of lacunary statistical convergence of order alpha and strongly q- summability of order alpha in partial metric spaces. We examine the inclusion relations linked to these concepts.Öğe On statistical convergence of order ? in partial metric spaces(Walter De Gruyter Gmbh, 2024) Bayram, Erdal; Bektas, Cigdem A.; Altin, YavuzThe present study introduces the notions of statistical convergence of order alpha and strong p-Cesaro summability of order alpha in partial metric spaces. Also, we examine the inclusion relations between these concepts. In addition, we introduce the notion of lambda-statistical convergence of order alpha in partial metric spaces while providing relations linked to these sequence spaces.Öğe On the invariant supspace problem(2013) Tonyalı, Cevriye; Bayram, ErdalIn this study, we present invariant subspaces (subideals) for a class of operators (positive operators) related to M-weakly and L-weakly compact operators. Principally, these invariant subspaces can be conceivable for all operators that commutes with any M-weakly or L-weakly compact operator. © 2013 Academic Publications, Ltd.Öğe On the Matrix Representations of Operators on the Classical Sequence Spaces(2019) Bayram, ErdalThe present study provides the necessary and sufficient conditions for the matrix characterizations of ??- and ??-weakly compact operators which are defined on certain classical sequence spaces as Banach lattices. It is knownthat these operators may coincide with both weakly compact and compact operators on Banach lattices. Ourstudy offers a different alternative to some known results for the matrix characterizations of compact andweakly compact operators which are presented in terms of L- and M-weakly compactness.Öğe On the Quotients of Regular Operators(Emrah Evren KARA, 2019) Bayram, Erdal; Binbaşıoglu, Cansu BinnazWe give some results about quotients of regular operators on Banach lattices by the linear span of the positive M-weakly and positive L-weakly compact operators. We also present a representation of the quotient space created by the linear span of the positive L-weakly compact operators. © 2019, Emrah Evren KARA. All rights reserved.Öğe Some compactness properties of L-weakly and M-weakly compact operators(Springer, 2012) Bayram, Erdal; Tonyali, C.We present some compactness properties of L-weakly and M-weakly compact operators on a Banach lattice under additional conditions. Thus, we can say that every bounded operator which commutes with any L-weakly or M-weakly compact operator have a non-trivial closed invariant subspace.Öğe Weighted statistical rough convergence in normed spaces(Maejo Univ, 2024) Bayram, Erdal; Aydin, Abdullah; Kucukaslan, MehmetStatistical convergence is a significant generalisation of the traditional convergence of real or complex valued sequences. Over the years, it has been studied by many authors and found many applications in various problems. In this paper we introduce a new concept about statistical rough convergence for sequences in normed spaces by using weighted density, which is a generalisation of the natural density. We investigate the fundamental properties of g-statistical rough convergence and statistical rough limit points including closeness, convexity and boundedness. We also establish a relationship between statistical rough limit points and g-statistical boundedness. The obtained results provide a new framework for studying statistical rough convergence.Öğe Weighted statistical rough convergence in normed spaces(Maejo University, 2024) Bayram, Erdal; Aydin, Abdullah; Kucukaslan, MehmetStatistical convergence is a significant generalisation of the traditional convergence of real or complex valued sequences. Over the years, it has been studied by many authors and found many applications in various problems. In this paper we introduce a new concept about statistical rough convergence for sequences in normed spaces by using weighted density, which is a generalisation of the natural density. We investigate the fundamental properties of g-statistical rough convergence and statistical rough limit points including closeness, convexity and boundedness. We also establish a relationship between statistical rough limit points and g-statistical boundedness. The obtained results provide a new framework for studying statistical rough convergence. © 2024 by Maejo University, San Sai, Chiang Mai, 50290 Thailand.
