• 대한수학회보
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• 제45권4호
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• pp.763-780
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• 2008

An Ostrowski type inequality is developed for estimating the deviation of the integral mean of an absolutely continuous function, and the linear combination of its values at k + 1 partition points, on a segment of (real) linear spaces. Several particular cases are provided which recapture some earlier results, along with the results for trapezoidal type inequalities and the classical Ostrowski inequality. Some inequalities are obtained by applying these results for semi-inner products; and some of these inequalities are proven to be sharp.

• Korean Journal of Mathematics
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• 제31권2호
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• pp.161-180
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• 2023

In this article, we will utilize (α, m)-convexity to create a new form of Simpson-Newton inequalities in quantum calculus by using q_𝝔1-integral and q_𝝔1-derivative. Newly discovered inequalities can be transformed into quantum Newton and quantum Simpson for generalized convexity. Additionally, this article demonstrates how some recently created inequalities are simply the extensions of some previously existing inequalities. The main findings are generalizations of numerous results that already exist in the literature, and some fundamental inequalities, such as Hölder's and Power mean, have been used to acquire new bounds.

• 대한수학회지
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• 제60권3호
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• pp.503-520
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• 2023

In this paper, using the theory of majorization, we discuss the Schur m power convexity for L-conjugate means of n variables and the Schur convexity for weighted L-conjugate means of n variables. As applications, we get several inequalities of general mean satisfying Schur convexity, and a few comparative inequalities about n variables Gini mean are established.

• International Journal of Contents
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• 제7권2호
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• pp.32-35
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• 2011

This research would be the first step toward in the long processes of proton technology industrial cluster development by focusing on the region's readiness and acceptability of the proton technology project. As is shown in our questionnaire survey, the top priorities needed to consider for the Proton Technology project are found to be job creation (mean 3.74), regional economic development (mean 3.72), industry infrastructure(3.54), institution for science and education(3.53), economic inequalities(3.33), tourism industry revitalization(3.20). For public servants top priorities in order found to be regional economic development, job creation, industry infrastructure, institution for science and education, economic inequalities, tourism industry revitalization. Universities' priorities in order found to be job creation, regional economic development, institution for science and education, industry infrastructure, economic inequalities, tourism industry revitalization. The mean reliability score for the each party was found to be mayor((3.04), citizens(2.99), province(2.97), private corporation(2.96), and universities((2.93). Of particular note, the mean score except the mayor were all below median (3.00). province(3.24), city council member(3.20), public employees (3.09), private corporation(3.03), nonprofit organization (2.97), mass media (2.96), citizens(2.96), and universities(2.89). The universities and colleges also should revise their strategic plans and thus restructure their internal academic programs, and must develop their own collaborative programs with Proton Engineering Frontier Project, related industries, city, and other government units. Not only educating, training, and providing top-notched man powers to the proton technology industries will be one of their primary missions.

• 호남수학학술지
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• 제45권2호
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• pp.340-358
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• 2023

This article establishes an equality for the case of twice-differentiable convex functions with respect to the conformable fractional integrals. With the help of this identity, we prove sundry midpoint-type inequalities by twice-differentiable convex functions according to conformable fractional integrals. Several important inequalities are obtained by taking advantage of the convexity, the Hölder inequality, and the power mean inequality. Using the specific selection of our results, we obtain several new and well-known results in the literature.

• 호남수학학술지
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• 제43권3호
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• pp.441-452
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• 2021

In this paper, improved power-mean integral inequality, which provides a better approach than power-mean integral inequality, is proved. Using Hölder-İşcan integral inequality and improved power-mean integral inequality, some inequalities of Hadamard's type for functions whose derivatives in absolute value at certain power are quasi-convex are given. In addition, the results obtained are compared with the previous ones. Then, it is shown that the results obtained together with identity are better than those previously obtained.

• Journal of applied mathematics & informatics
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• 제41권5호
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• pp.963-972
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• 2023

In this paper, geometrically convex and s-convex functions in third and fourth sense are merged to form (g, s)-convex function. Characterizations of (g, s)-convex function, algebraic and functional properties are presented. In addition, novel functions based on the integral of (g, s)-convex functions in the third sense are created, and inequality relations for these functions are explored and examined under particular conditions. Further, there are also some relationships between (g, s)-convex function and previously defined functions. The (g, s)-convex function and its derivatives will then be used to extend the well-known H-H and Fejer's type inequalities. In order to obtain the previously mentioned conclusions, several special cases from previous literature for extended H-H and Fejer's inequalities are also investigated. The relation between the average (mean) values and newly created H-H and Fejer's inequalities are also examined.

• 대한수학회보
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• 제38권4호
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• pp.701-708
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• 2001

In this article, using the properties of power mean, some new generalizations of the strengthened Hardy's inequalities are given.

• Journal of applied mathematics & informatics
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• 제41권6호
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• pp.1181-1191
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• 2023

This paper investigates Young inequalities for matrices, a problem closely linked to operator theory, mathematical physics, and the arithmetic-geometric mean inequality. By obtaining new inequalities for unitarily invariant norms, we aim to derive a fresh Young inequality specifically designed for matrices.To lay the foundation for our study, we provide an overview of basic notation related to matrices. Additionally, we review previous advancements made by researchers in the field, focusing on Young improvements.Building upon this existing knowledge, we present several new enhancements of the classical Young inequality for nonnegative real numbers. Furthermore, we establish a matrix version of these improvements, tailored to the specific characteristics of matrices. Through our research, we contribute to a deeper understanding of Young inequalities in the context of matrices.

• Kyungpook Mathematical Journal
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• 제53권3호
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• pp.479-495
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• 2013

Taking the weighted geometric mean [11] on the cone of positive definite matrix, we propose an iterative mean algorithm involving weighted arithmetic and geometric means of $n$-positive definite matrices which is a weighted version of Carlson mean presented by Lee and Lim [13]. We show that each sequence of the weigthed Carlson iterative mean algorithm has a common limit and the common limit of satisfies weighted multidimensional versions of all properties like permutation symmetry, concavity, monotonicity, homogeneity, congruence invariancy, duality, mean inequalities.