• Honam Mathematical Journal
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• v.42 no.2
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• pp.391-409
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• 2020

In the current paper, the intuitionistic fuzzy normed space version of Hyers-Ulam stability for multi-additive, multi-cubic and multi-additive-cubic mappings by using a fixed point method are studied. Moreover, a few corollaries corresponding to some known stability and hyperstability outcomes in intuitionistic fuzzy normed space are presented.

• Communications of the Korean Mathematical Society
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• v.39 no.1
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• pp.127-135
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• 2024

In this paper, we improve Corollary 1 of [4] and then present an example to show that the assertion in the mentioned corollary can not be valid in the singularity case.

• Communications of the Korean Mathematical Society
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• v.39 no.3
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• pp.673-692
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• 2024

In this work, an alternative fashion of the multi-Jensen is introduced. The structures of the multi-Jensen and the multi-Euler-Lagrange-Jensen mappings are described. In other words, the system of n equations defining each of the mentioned mappings is unified as a single equation. Furthermore, by applying a fixed point theorem, the Hyers-Ulam stability for the multi-Euler-Lagrange-Jensen mappings in the setting of Banach spaces is established. An appropriate counterexample is supplied to invalidate the results in the case of singularity for multiadditive mappings.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.517-522
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• 2006

In this paper, we obtain the general solution and the generalized Hyers-Ulam stability of the multi-additive functional equation $f(x1+x2,y1+y2,z1+z2)={\Sigma}_{1{\le}i,j,k{\le}2}\;f(x1,yj,zk)$.

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.319-333
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• 2013

Using the fixed point method, we prove the generalized Hyers-Ulam-Rassias stability of the following functional equation in multi-Banach spaces: $${\sum_{1{\leq}i_<j{\leq}n}}\;f(\frac{r_ix_i+r_jx_j}{k})=\frac{n-1}{k}{\sum_{i=1}^n}r_if(x_i)$$.

• The Pure and Applied Mathematics
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• v.13 no.4 s.34
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• pp.295-301
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• 2006

We Investigate the relation between the multi-variable bi-additive functional equation f(x+y+z,u+v+w)=f(x,u)+f(x,v)+f(x,w)+f(y,u)+f(y,v)+f(y,w)+f(z,u)+f(z,v)+f(z,w) and the multi-variable quadratic functional equation g(x+y+z)+g(x-y+z)+g(x+y-z)+g(-x+y+z)=4g(x)+4g(y)+4g(z). Furthermore, we find out the general solution of the above two functional equations.

• Communications of the Korean Mathematical Society
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• v.23 no.2
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• pp.191-199
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• 2008

We investigate the relation between the vector variable bi-additive functional equation $f(\sum\limits^n_{i=1} xi,\;\sum\limits^n_{i=1} yj)={\sum\limits^n_{i=1}\sum\limits^n_ {j=1}f(x_i,y_j)$ and the multi-variable quadratic functional equation $$g(\sum\limits^n_{i=1}xi)\;+\;\sum\limits_{1{\leq}i<j{\leq}n}\;g(x_i-x_j)=n\sum\limits^n_{i=1}\;g(x_i)$$. Furthermore, we find out the general solution of the above two functional equations.

• Bulletin of the Korean Mathematical Society
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• v.45 no.4
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• pp.729-737
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• 2008

In this paper we characterize multi-Jensen functions f : $V^n\;{\rightarrow}\;W$, where n is a positive integer, V, W are commutative groups and V is uniquely divisible by 2. Moreover, under the assumption that f : $\mathbb{R}\;{\rightarrow}\;\mathbb{R}$ is Borel measurable, we obtain representation of f (respectively, f, g, h : $\mathbb{R}\;{\rightarrow}\;\mathbb{R}$) such that the Jensen difference $$2f\;\(\frac{x\;+\;y}{2}\)\;-\;f(x)\;-\;f(y)$$ (respectively, the Pexider difference $$2f\;\(\frac{x\;+\;y}{2}\)\;-\;g(x)\;-\;h(y))$$ takes values in a countable subgroup of $\mathbb{R}$.

• Asian-Australasian Journal of Animal Sciences
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• v.16 no.8
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• pp.1087-1092
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• 2003

As an experimental reference population, crosses between Korean native pig and Landraces were established and information on growth traits was recorded. Animals were genotyped for 24 microsatellite markers covering chromosomes 2, 6, and 7 for partial-genome scan to identify chromosomal regions that have effects on growth traits. quantitative trait loci (QTL) effects were estimated using interval mapping by the regression method under the line cross models with a test for imprinting effects. For test of presence of QTL, chromosome-wide and single position significance thresholds were estimated by permutation test and normal significance threshold for the imprinting test were derived. For tests against the Mendelian model, additive and dominance coefficients were permuted within individuals. Thresholds (5% chromosome-wide) against the no-QTL model for the analyzed traits ranged from 4.57 to 4.99 for the Mendelian model and from 4.14 to 4.67 for the imprinting model, respectively. Partial-genome scan revealed significant evidence for 4 QTL affecting growth traits, and 2 out of the 4 QTLs were imprinted. This study demonstrated that testing for imprinting should become a standard procedure to unravel the genetic control of multi-factorial traits. The models and tests developed in this study allowed the detection and evaluation of imprinted QTL.

• Mycobiology
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• v.49 no.6
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• pp.589-598
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• 2021

White strains of Hypsizygus marmoreus are more difficult to cultivate than are brown strains; therefore, new white strain breeding strategies are required. Accordingly, we constructed the genetic map of H. marmoreus with 1996 SNP markers on 11 linkage groups (LGs) spanning 1380.49 cM. Prior to analysis, 82 backcrossed strains (HM8 lines) were generated by mating between KMCC03106-31 and the progenies of the F1 hybrid (Hami-18 × KMCC03106-93). Using HM8, the first 23 quantitative trait loci (QTLs) of yield-related traits were detected with high limit of detection (LOD) scores (1.98-9.86). The length, thickness, and hardness of the stipe were colocated on LG 1. Especially, length of stipe and thickness of stipe were highly correlated given that the correlation coefficients were negative (-0.39, p value ≤ .01). And a typical biomodal distribution was observed for lightness of the pileus and the lightness of the pileus trait belonged to the LG 8, as did traits of earliness and mycelial growth in potato dextrose agar (PDA) medium. Therefore, results for color traits can be suggested that color is controlled by a multi-gene of one locus. The yield trait was highly negatively correlated with the traits for thickness of the stipe (-0.45, p value ≤ .01). Based on additive effects, the white strain was confirmed as recessive; however, traits of mycelial growth, lightness, and quality were inherited by backcrossed HM8 lines. This new genetic map, finely mapped QTLs, and the strong selection markers could be used in molecular breeding of H. marmoreus.