• Kyungpook Mathematical Journal
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• 제59권1호
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• pp.101-123
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• 2019

In this paper, we consider a system of nonlinear variational type inclusions involving ($H,{\varphi},{\eta}$)-monotone operators in real Banach spaces. Further, we define a proximal operator associated with an ($H,{\varphi},{\eta}$)-monotone operator and show that it is single valued and Lipschitz continuous. Using proximal point operator techniques, we prove the existence and uniqueness of a solution and suggest an iterative algorithm for the system of nonlinear variational type inclusions. Furthermore, we discuss the convergence of the iterative sequences generated by the algorithms.

• 대한수학회논문집
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• 제39권1호
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• pp.137-147
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• 2024

In the present paper, we introduce a new class of operators called p-demicompact operators between two lattice normed spaces X and Y. We study the basic properties of this class. Precisely, we give some conditions under which a p-bounded operator be p-demicompact. Also, a sufficient condition is given, under which each p-demicompact operator has a modulus which is p-demicompact. Further, we put in place some properties of this class of operators on lattice normed spaces.

• 대한수학회지
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• 제60권1호
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• pp.33-69
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• 2023

Let α ∈ (0, ∞), p ∈ (0, ∞) and q(·) : ℝⁿ → [1, ∞) satisfy the globally log-Hölder continuity condition. We introduce the weak Herz-type Hardy spaces with variable exponents via the radial grand maximal operator and to give its maximal characterizations, we establish a version of the boundedness of the Hardy-Littlewood maximal operator M and the Fefferman-Stein vector-valued inequality on the weak Herz spaces with variable exponents. We also obtain the atomic and the molecular decompositions of the weak Herz-type Hardy spaces with variable exponents. As an application of the atomic decomposition we provide various equivalent characterizations of our spaces by means of the Lusin area function, the Littlewood-Paley g-function and the Littlewood-Paley $g^*_{\lambda}$-function.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제11권1호
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• pp.54-58
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• 2011

In this paper, we use L-fuzzy preopen operator to introduce the degree of pre-separatedness and the degree of preconnectedness in L-fuzzy topological spaces. Many characterizations of the degree of preconnectedness are presented in L-fuzzy topological spaces.

• Korean Journal of Mathematics
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• 제30권1호
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• pp.147-154
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• 2022

In this article, we prove that an absolutely summing operator on 𝓛^λ₁ spaces has a lifting under the conditions that a target Banach space is a quotient of reflexive Banach subspaces.

• 대한수학회보
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• 제60권3호
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• pp.649-657
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• 2023

In this paper, we give new necessary and sufficient conditions for the compactness of composition operator on the Besov space and the Bloch space of the unit ball, which, to a certain extent, generalizes the results given by M. Tjani in [10].

• 대한수학회지
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• 제56권2호
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• pp.523-537
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• 2019

We estimate the essential norms of Volterra-type integral operators $V_g$ and $I_g$, and multiplication operators $M_g$ with holomorphic symbols g on a large class of generalized Fock spaces on the complex plane ${\mathbb{C}}$. The weights defining these spaces are radial and subjected to a mild smoothness conditions. In addition, we assume that the weights decay faster than the classical Gaussian weight. Our main result estimates the essential norms of $V_g$ in terms of an asymptotic upper bound of a quantity involving the inducing symbol g and the weight function, while the essential norms of $M_g$ and $I_g$ are shown to be comparable to their operator norms. As a means to prove our main results, we first characterized the compact composition operators acting on the spaces which is interest of its own.

• East Asian mathematical journal
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• 제29권3호
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• pp.315-326
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• 2013

In this paper, a new monotonicity, $M({\cdot},{\cdot})$-monotonicity, is introduced in Banach spaces, and the resolvent operator of an $M({\cdot},{\cdot})$-monotone operator is proved to be single valued and Lipschitz continuous. By using the resolvent operator technique associated with $M({\cdot},{\cdot})$-monotone operators, we construct a proximal point algorithm for solving a class of variational inclusions. And we prove the convergence of the sequences generated by the proximal point algorithms in Banach spaces. The results in this paper extend and improve some known results in the literature.

• East Asian mathematical journal
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• 제28권1호
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• pp.37-47
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• 2012

In this paper, we study generalized implicit variational-like inclusions and $J^{\eta}$-proximal operator equations in Banach spaces. It is established that generalized implicit variational-like inclusions in real Banach spaces are equivalent to fixed point problems. We also establish relationship between generalized implicit variational-like inclusions and $J^{\eta}$-proximal operator equations. This equivalence is used to suggest a iterative algorithm for solving $J^{\eta}$-proximal operator equations.

• 대한수학회보
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• 제48권6호
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• pp.1195-1205
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• 2011

Let $H(\mathbb{D})$ denote the class of all analytic functions on the open unit disk $\mathbb{D}$ of the complex plane $\mathbb{C}$. Let n be a nonnegative integer, ${\varphi}$ be an analytic self-map of $\mathbb{D}$ and $u{\in}H(\mathbb{D})$. The generalized weighted composition operator is defined by $$D_{{\varphi},u}^nf=uf^{(n)}{\circ}{\varphi},\;f{\in}H(\mathbb{D})$$. The boundedness and compactness of the generalized weighted composition operator from area Nevanlinna spaces to weighted-type spaces and little weighted-type spaces are characterized in this paper.