• Kyungpook Mathematical Journal
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• v.59 no.2
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• pp.233-240
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• 2019

In the present paper, absolute matrix summability of infinite series is studied. A new theorem concerning absolute matrix summability factors, which generalizes a known theorem dealing with absolute Riesz summability factors of infinite series, is proved using almost increasing and ${\delta}$-quasi-monotone sequences. Also, a result dealing with absolute $Ces{\grave{a}}ro$ summability is given.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.283-288
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• 2022

In this paper we characterize the sets of summability factors (|C, 0|_k, |R, p_n|_s) and (|R, p_n|_k, |C, 0|_s), 1 < k ≤ s < ∞, which also extends some known results.

• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.1-9
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• 2023

In the present paper, two theorems on absolute matrix summability of infinite series are generalized for the 𝜑 - |A, p_n|_k summability method using quasi 𝛽-power increasing sequences instead of almost increasing sequences.

• Journal of applied mathematics & informatics
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• v.39 no.1_2
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• pp.117-124
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• 2021

We obtain a new matrix generalization result dealing with weighted mean summability of infinite series by using a new general class of power increasing sequences obtained by Sulaiman [9]. This theorem also includes some new and known results dealing with some basic summability methods.

• Journal of the Korean Mathematical Society
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• v.15 no.2
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• pp.167-176
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• 1979

• Korean Journal of Mathematics
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• v.32 no.3
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• pp.545-560
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• 2024

In the present study, we have constructed a new Banach series space |𝛶^r|^u_p by using concept of absolute Jordan totient summability |𝛶^r, u_n|_p which is derived by the infinite regular matrix of the Jordan's totient function. Also, we prove that the series space |𝛶^r|^u_p is linearly isomorphic to the space of all p-absolutely summable sequences ℓ_p for p ≥ 1. Moreover, we compute the α-, β- and γ- duals of this space and construct Schauder basis for the series space |𝛶^r|^u_p. Finally, we characterize the classes of infinite matrices (|𝛶^r|^u_p, X) and (X, |𝛶^r|^u_p), where X is any given classical sequence spaces ℓ_∞, c, c₀ and ℓ₁.

• Korean Journal of Mathematics
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• v.28 no.2
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• pp.205-221
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• 2020

Paranormed spaces are important as a generalization of the normed spaces in terms of having more general properties. The aim of this study is to introduce a new paranormed space |𝜙_z|(p) over the paranormed space ℓ(p) using Euler totient means, where p = (p_k) is a bounded sequence of positive real numbers. Besides this, we investigate topological properties and compute the α-, β-, and γ duals of this paranormed space. Finally, we characterize the classes of infinite matrices (|𝜙_z|(p), λ) and (λ, |𝜙_z|(p)), where λ is any given sequence space.