• Bulletin of the Korean Mathematical Society
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• v.37 no.3
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• pp.569-575
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• 2000

In this paper, a unique common fixed point theorem for a sequence of mutually contractive and commuting sequence of self mappings on Menger spaces has been proved.

• Communications of the Korean Mathematical Society
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• v.25 no.1
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• pp.51-57
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• 2010

In this paper we introduce and study the lacunary strong Zweier sequence spaces $N_{\theta}^O[Z]$, $N_{\theta}[Z]$ consisting of all sequences x = $(x_k)$ such that (Zx) in the space $N_{\theta}$ and $N_{\theta}^O$ respectively, which is normed. Also, prove that $N_{\theta}^O[Z}$, $N_{\theta}[Z}$, are linearly isomorphic to the space $N_{\theta}^O$ and $N_{\theta}$, respectively. And we study some connections between lacunary strong Zweier sequence and lacunary statistical Zweier convergence sequence.

• Journal of the Korean Mathematical Society
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• v.55 no.4
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• pp.809-832
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• 2018

In this paper, we form the basis of the abstract theory for constructing the $K{\ddot{u}}nneth$ spectral sequence for a complex of Banach spaces. As the category of Banach spaces is not abelian, several difficulties occur and hinder us from applying the usual method of homological algebra directly. The most notable facts are the image of a morphism of Banach spaces is not necessarily a Banach space, and also the closed summand of a Banach space need not be a topological direct summand. So, we consider some conditions and categorical terms that fit the category of Banach spaces to modify the familiar method of homological algebra.

• 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.63 no.3
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• pp.451-461
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• 2023

In this paper, we study the fixed point property for generalized asymptotically nonexpansive mappings in the setting of p-Hadamard spaces, with p ≥ 2. We prove the strong convergence of the sequence generated by the modified two-step iterative sequence for finding a fixed point of a generalized asymptotically nonexpansive mapping in p-Hadamard spaces.

• Kyungpook Mathematical Journal
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• v.50 no.3
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• pp.389-397
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• 2010

In this paper we introduce the new generalized difference sequence space $\ell_\infty$($\Delta_v^n$, M,p,q,s), $\bar{c}$($\Delta_v^n$,M,p,q,s), $\bar{c_0}$($\Delta_v^n$,M,p,q,s), m($\Delta_v^n$,M,p,q,s) and $m_0$($\Delta_v^n$,M,p,q,s) defined over a seminormed sequence space (X,q). We study some of it properties, like completeness, solidity, symmetricity etc. We obtain some relations between these spaces as well as prove some inclusion result.

• Journal of applied mathematics & informatics
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• v.37 no.5_6
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• pp.329-339
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• 2019

The Banach spaces $m^p(\phi)$ and $n^p(\phi)$ are very important sequence spaces related to $l_p$, which were defined to fill the gaps between $l_p(1{\leq}p{\leq}{\infty})$. In this paper, we investigated the solubility of the infinite system of differential equations in $m^p(\phi)$ and $n^p(\phi)$ by proving related theorems. Moreover, one example has been included for the justification of the claim of this paper.

• Korean Journal of Mathematics
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• v.29 no.1
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• pp.25-40
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• 2021

In this article we introduce tribonacci sequence spaces c0(T) and c(T) derived by the domain of a newly defined regular tribonacci matrix T. We give some topological properties, inclusion relations, obtain the Schauder basis and determine ��-, ��- and ��- duals of the spaces c0(T) and c(T). We characterize certain matrix classes (c0(T), Y) and (c(T), Y), where Y is any of the spaces c0, c or ℓ∞. Finally, using Hausdorff measure of non-compactness we characterize certain class of compact operators on the space c0(T).

• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.261-272
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• 2006

In this paper, we define the sequence spaces: $[V,{\lambda},f,p]_0({\Delta}^r,E,u),\;[V,{\lambda},f,p]_1({\Delta}^r,E,u),\;[V,{\lambda},f,p]_{\infty}({\Delta}^r,E,u),\;S_{\lambda}({\Delta}^r,E,u),\;and\;S_{{\lambda}0}({\Delta}^r,E,u)$, where E is any Banach space, and u = ($u_k$) be any sequence such that $u_k\;{\neq}\;0$ for any k , examine them and give various properties and inclusion relations on these spaces. We also show that the space $S_{\lambda}({\Delta}^r, E, u)$ may be represented as a $[V,{\lambda}, f, p]_1({\Delta}^r, E, u)$ space. These are generalizations of those defined and studied by M. Et., Y. Altin and H. Altinok [7].

• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.633-642
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• 1995

Recently S. Axler proved that every sequence in the unit disk U converging to the boundary contains an interpolating subsequence for the multipliers of the Dirichlet space D(U). In this paper we generalizes Axler's result to the finitely connected planer domains such that the Dirichlet spaces are contained in the Bergman spaces.