• Honam Mathematical Journal
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• v.41 no.4
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• pp.725-744
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• 2019

In this paper we introduce some new types of double difference sequence spaces defined by a new definition of convergence of double sequences and a double series with the help of sequence of Orlicz functions and a four dimensional bounded regular matrices A = (a_rtkl). We also make an effort to study some topological properties and inclusion relations between these sequence spaces. Finally, we compute the closed ideals in the space 𝑙²_∞.

• Journal of the Korean Mathematical Society
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• v.60 no.5
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• pp.1057-1072
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• 2023

Let 𝜑 : ℝⁿ × [0, ∞) → [0, ∞) be a growth function and H^𝜑(ℝⁿ) the Musielak-Orlicz Hardy space defined via the non-tangential grand maximal function. A general summability method, the so-called 𝜃-summability is considered for multi-dimensional Fourier transforms in H^𝜑(ℝⁿ). Precisely, with some assumptions on 𝜃, the authors first prove that the maximal operator of the 𝜃-means is bounded from H^𝜑(ℝⁿ) to L^𝜑(ℝⁿ). As consequences, some norm and almost everywhere convergence results of the 𝜃-means, which generalizes the well-known Lebesgue's theorem, are then obtained. Finally, the corresponding conclusions of some specific summability methods, such as Bochner-Riesz, Weierstrass and Picard-Bessel summations, are also presented.

• Honam Mathematical Journal
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• v.37 no.4
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• pp.505-512
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• 2015

In this note we find the upper bound for ${\rho}(u^n,M)=\int_{0}^{T}\int_{0}^{{\mid}u(t){\mid}^n}p(s)dsdt$ and show that $F(y)=y^n$ is $m_{\phi}^M$-Bochner integrable on $C(\mathcal{O} _M)$ for $0{\leq}t{\leq}T$ when $\int_{\mathcal{O}_M}{\parallel}u_0{\parallel}_M^nd{\phi}(u_0)$ is finite.

• Kyungpook Mathematical Journal
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• v.53 no.3
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• pp.319-332
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• 2013

The sequence space $m(M,{\phi})^F$ of fuzzy real numbers is introduced. Some properties of this sequence space like solidness, symmetricity, convergence-free etc. are studied. We obtain some inclusion relations involving this sequence space.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.155-167
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• 2019

In this article we are concerned with some non-local problems of Kirchhoff type with Dirichlet boundary condition in Orlicz-Sobolev spaces. A result of the existence of infinitely many solutions is established using variational methods and Ricceri's critical points principle modified by Bonanno.

• Journal of applied mathematics & informatics
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• v.37 no.5_6
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• pp.459-467
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• 2019

In this work, via Orlicz functions, we have obtained a generalization of rough statistical convergence of asymptotically equivalent triple sequences a new non-matrix convergence method, which is intermediate between the ordinary convergence and the rough statistical convergence. We also have examined some inclusion relations related to this concept. We obtain the results are non negative real numbers with respect to the partial order on the set of real numbers.

• Journal of applied mathematics & informatics
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• v.37 no.1_2
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• pp.37-52
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• 2019

In this paper we introduce a new concept for Riesz almost lacunary ${\chi}^3$ sequence spaces strong P - convergent to zero with respect to an Orlicz function and examine some properties of the resulting sequence spaces. We introduce and study statistical convergence of Riesz almost lacunary ${\chi}^3$ sequence spaces and some inclusion theorems are discussed.

• Nonlinear Functional Analysis and Applications
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• v.27 no.3
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• pp.649-662
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• 2022

This paper is concerned with the existence of solutions for a class of 𝚽-Kirchhoff type equations with critical exponent in Orlicz-Sobolev spaces. Our technical approach is based on variational methods.

• Bulletin of the Korean Mathematical Society
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• v.60 no.5
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• pp.1391-1408
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• 2023

Let M and M^# be Hardy-Littlewood maximal operator and sharp maximal operator, respectively. In this article, we present necessary and sufficient conditions for the boundedness properties for commutator operators [M, b] and [M^#, b] in a general context of Banach function spaces when b belongs to BMO(?ⁿ) spaces. Some applications of the results on weighted Lebesgue spaces, variable Lebesgue spaces, Orlicz spaces and Musielak-Orlicz spaces are also given.

• Bulletin of the Korean Mathematical Society
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• v.17 no.1
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• pp.39-41
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• 1980