• Korean Journal of Mathematics
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• v.29 no.2
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• pp.211-225
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• 2021

In the present paper we introduce some sequence spaces over n-normed spaces defined by fractional difference operator and Musielak-Orlicz function 𝓜 = (𝕱_i). We also study some topological properties and prove some inclusion relations between these spaces.

• Kyungpook Mathematical Journal
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• v.52 no.2
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• pp.137-147
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• 2012

In this paper we introduce some new double sequence spaces via ideal convergence and an Orlicz function in $n$-normed spaces and examine some properties of the resulting spaces.

• Journal of applied mathematics & informatics
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• v.32 no.5_6
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• pp.687-695
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• 2014

In this article we introduce the zweier double sequence spaces $_2Z^I$(M), $_2Z_0^I$(M) and $_2Z_{\infty}^I$(M) using the Orlicz function M. We study the algebraic properties and inclusion relations on these spaces.

• Kyungpook Mathematical Journal
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• v.48 no.4
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• pp.613-622
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• 2008

In this article we introduce some difference sequence spaces defined by Orlicz function and study different properties of these spaces like completeness, solidity, symmetricity etc. We establish some inclusion results among them.

• Kyungpook Mathematical Journal
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• v.54 no.1
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• pp.73-86
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• 2014

In the present paper we introduce difference paranormed sequence spaces $c_0(\mathcal{M},{\Delta}^n_m,p,u,{\parallel}{\cdot},{\cdots},{\cdot}{\parallel})$, $c(\mathcal{M},{\Delta}^n_m,p,u,{\parallel}{\cdot},{\cdots},{\cdot}{\parallel})$ and $l_{\infty}(\mathcal{M},{\Delta}^n_m,p,u,{\parallel}{\cdot},{\cdots},{\cdot}{\parallel})$ defined by a Musielak-Orlicz function $\mathcal{M}$ = $(M_k)$ over n-normed spaces. We also study some topological properties and some inclusion relations between these spaces.

• Communications of the Korean Mathematical Society
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• v.36 no.1
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• pp.121-134
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• 2021

In this paper we introduce the notion of paranormed p-absolutely convergent and paranormed Cesro summable sequences of complex uncertain variables with respect to measure, mean, distribution etc. defined by on Orlicz function. We have established some relationships among these notions as well as with other classes of complex uncertain variables.

• Journal of the Korean Mathematical Society
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• v.59 no.6
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• pp.1139-1151
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• 2022

This paper studies the eigenvalues of the G(·)-Laplacian Dirichlet problem $$\{-div\;\(\frac{g(x,\;{\mid}{\nabla}u{\mid})}{{\mid}{\nabla}u{\mid}}{\nabla}u\)={\lambda}\;\(\frac{g(x,{\mid}u{\mid})}{{\mid}u{\mid}}u\)\;in\;{\Omega}, \\u\;=\;0\;on\;{\partial}{\Omega},$$ where Ω is a bounded domain in ℝ^N and g is the density of a generalized Φ-function G(·). Using the Lusternik-Schnirelmann principle, we show the existence of a nondecreasing sequence of nonnegative eigenvalues.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.689-695
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• 2014

Let M be an N-function satisfies the ${\Delta}_2$-condition and let $O_M$ be the Orlicz space associated with M. Let $C(O_M)$ be the space of all continuous functions defined on the interval [0, T] with values in $O_M$. In this note, we define the analogue of Wiener measure $m^M_{\phi}$ on $C(O_M)$, establish the Wiener integration formulae for the cylinder functions on $C(O_M)$ and give some examples related to our formulae.

• Journal of the Korean Mathematical Society
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• v.58 no.2
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• pp.383-400
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• 2021

The aim of this paper is to mainly establish the sufficient and necessary conditions for the boundedness of the commutator ����Ω,b which is generated by the parameter Marcinkiwicz integral ����Ω and the Lipschitz function b on generalized Orlicz-Morrey space L��,��(Rd) in the sense of the Adams type result (or Spanne type result). Moreover, the necessary conditions for the parameter Marcinkiewizcz integral ����Ω on the L��,��(Rd), and the commutator [b,����Ω] generated by the ����Ω and the space BMO on the L��,��(Rd), are also obtained, respectively.

• 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.