• 대한수학회보
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• 제60권6호
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• pp.1477-1496
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• 2023

A class of normalized univalent functions f defined in an open unit disk of the complex plane is introduced and studied such that the values of the quantity zf'(z)/f(z) lies inside the evolute of a nephroid curve. The inclusion relations of the newly defined class with other subclasses of starlike functions and radius problems concerning the second partial sums are investigated. All the obtained results are sharp.

• Industrial Engineering and Management Systems
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• 제10권1호
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• pp.65-73
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• 2011

In rough set literatures, methods for inducing minimal rules from a given decision table have been proposed. When the decision attribute is ordinal, inducing rules about upward and downward unions of decision classes is advantageous in the simplicity of obtained rules. However, because of independent applications of the rule induction method, inclusion relations among upward/downward unions in conclusion parts are not inherited to the condition parts of obtained rules. This non-inheritance may debase the quality of obtained rules. To ensure that inclusion relations among conclusions are inherited to conditions, we propose two rule induction approaches. The performances of the proposed approaches considering the inclusion relations between conclusions are examined by numerical experiments.

• 대한수학회보
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• 제42권3호
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• pp.623-629
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• 2005

Inclusion relations under certain integral operators are proved for k-uniformly starlike functions. These results are also extended to k-uniformly convex, close-to-convex, and quasi-convex functions

• 대한수학회논문집
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• 제35권3호
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• pp.843-854
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• 2020

The purpose of this present paper is to obtain inclusion relations between various subclasses of harmonic univalent functions by using the convolution operator associated with generalized distribution series. To be more precise, we obtain such inclusions with harmonic starlike and harmonic convex mappings in the plane.

• 대한수학회보
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• 제48권4호
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• pp.689-695
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• 2011

The main object of this paper is to prove several inclusion relations associated with (j, ${\delta}$)-neighborhoods of various subclasses defined by Salagean operator by making use of the familiar concept of neighborhoods of analytic functions. Special cases of some of these inclusion relations are shown to yield known results.

• Kyungpook Mathematical Journal
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• 제54권2호
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• pp.211-220
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• 2014

In the present investigation, by making use of the familiar concept of neighborhoods of analytic and multivalent functions, we prove several inclusion relations associated with the (n, ${\delta}$)-neighborhoods of certain subclasses of analytic functions of complex order, which are introduced here by means of the Al-Oboudi derivative. Several special cases of the main results are mentioned.

• 대한수학회지
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• 제58권5호
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• pp.1147-1180
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• 2021

By considering the polynomial function 𝜙_car(z) = 1 + z + z²/2, we define the class 𝓢^*_car consisting of normalized analytic functions f such that zf'/f is subordinate to 𝜙_car in the unit disk. The inclusion relations and various radii constants associated with the class 𝓢^*_car and its connection with several well-known subclasses of starlike functions is established. As an application, the obtained results are applied to derive the properties of the partial sums and convolution.

• 대한기계학회논문집A
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• 제23권6호
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• pp.968-978
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• 1999

The effective elastic properties of materials containing spherical inclusions were calculated by the elastic wave scattering theory. In the formulation additional scattering fields by the presence of random multiple scatterers that affects the effective properties were found by the single scattering approximation. In calculating the scattering fields the ensemble average on the displacements and strains inside the scatterer was found from the static approximation at long wavelength limit. The displacements were assumed to be equal to the incident field, while the strains were calculated by Eshelby's equivalent inclusion principle on the single inclusion problem. Four different models were considered and they reflected different degrees of multiple scattering effects based on the approximation introduced in the process of embedding the inclusion in the matrix. The expressions for the effective elastic constants were given in each model, and their relations to the results obtained from other scattering theory and elasticity theory were discussed. The theoretical predictions were compared with experimental results on the epoxy matrix composites containing tungsten particles of different sizes and volume fractions

• Kyungpook Mathematical Journal
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• 제46권4호
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• pp.591-595
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• 2006

In this paper, we define ${\Delta}^m$-Lacunary strongly convergent sequences defined by sequence of moduli and give various properties and inclusion relations on these sequence spaces.

• Korean Journal of Mathematics
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• 제29권1호
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• pp.169-177
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• 2021

The aim of the present study is to introduce the concepts of deferred statistical convergence, deferred statistical Cauchy sequence and deferred Cesàro summability in paranormed spaces. We investigate some properties of these concepts and some inclusion relations with examples.