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The above results only involve a single mapping, we will consider an infinite family of mappings in this paper.
For the uniqueness of the fixed point of a generalized Meir-Keeler α-contractive mapping, we will consider the following hypothesis.
For the uniqueness of a fixed point of a generalized α-ψ-ϕ contractive mapping, we will consider the following hypothesis.
for a mapping We will prove the stability in normed group by using shadowing property and also the Hyers-Ulam stability of each functional equation in Banach spaces.
For the uniqueness of a fixed point of α-ψ-Geraghty contraction and generalized α-ψ-Geraghty contraction mapping, we will consider the following condition.
For the uniqueness of a fixed point of a generalized α-ψ-contractive mapping, we will consider the following hypothesis, in which Fix ( T ) denotes the set of all fixed points of T.
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As only approximately one quarter of the SNPs were mapped we will report both the number of mapped SNPs and the total number of SNPs that were significant for any statistical test.
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To address that problem, in this part of our series, we will present and describe demographic patterns for five major ethno-racial groups, both presently and historically.1 In some cases, the maps we will introduce in this brief even better illustrate the degree of racial isolation and concentration experienced by different groups than the segregation maps.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com