On Orlicz-Power Series Spaces

Karapınar, Erdal; Zakharyuta, Vyacheslav

doi:10.1007/s00009-010-0051-2

Cited by 3 publications

(1 citation statement)

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“…Moreover, they showed the existence of a fixed point of Kannan pre-quasinorm contraction maps on it and on the prequasi-Banach operator ideal constructed by s-numbers which belong to this sequence space. For more details on Kannan's fixed point theorems, see [17][18][19][20][21][22][23][24]. The aim of this paper is to examine the concept of the pre-quasinorm on ℓðrÞ with a variable exponent in ð1, ∞Þ.…”

Section: Introductionmentioning

confidence: 99%

Some Fixed Point Results of Kannan Maps on the Nakano Sequence Space

Bakery

Mohamed

2021

Journal of Function Spaces

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In the recent past, some researchers studied some fixed point results on the modular variable exponent sequence space ℓ r . ψ , where ψ v = ∑ a = 0 ∞ 1 / r a v a r a and r a ≥ 1 . They depended on their proof that the modular ψ has the Fatou property. But we have explained that this result is incorrect. Hence, in this paper, the concept of the premodular, which generalizes the modular, on the Nakano sequence space such as its variable exponent in 1 , ∞ and the operator ideal constructed by this sequence space and s -numbers is introduced. We construct the existence of a fixed point of Kannan contraction mapping and Kannan nonexpansive mapping acting on this space. It is interesting that several numerical experiments are presented to illustrate our results. Additionally, some successful applications to the existence of solutions of summable equations are introduced. The novelty lies in the fact that our main results have improved some well-known theorems before, which concerned the variable exponent in the aforementioned space.

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