• Korean Journal of Mathematics
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• v.29 no.2
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• pp.293-304
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• 2021

In this paper, we present a Schwarz lemma at the boundary for analytic functions at the unit disc, which generalizes classical Schwarz lemma for bounded analytic functions. For new inequalities, the results of Rogosinski's lemma, Subordination principle and Jack's lemma were used.

• The Pure and Applied Mathematics
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• v.28 no.3
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• pp.235-246
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• 2021

In this study, a Schwarz lemma at the boundary for analytic functions at the unit disc, which generalizes classical Schwarz lemma for bounded analytic functions, is considered.The results of Rogosinskis lemma and Jacks lemma have been utilized to derive novel inequalities. Also, these inequalities have been strengthened by considering the critical points which are different from zero.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.2053-2059
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• 2013

In this paper, a boundary version of the Schwarz lemma is investigated. We obtain more general results at the boundary. Also, new inequalities of the Schwarz lemma at boundary is obtained and the sharpness of these inequalities is proved.

• The Pure and Applied Mathematics
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• v.27 no.4
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• pp.157-169
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• 2020

In this paper, we improve a new boundary Schwarz lemma, for analytic functions in the unit disk. For new inequalities, the results of Rogosinski's lemma, Subordinate principle and Jack's lemma were used. Moreover, in a class of analytic functions on the unit disc, assuming the existence of angular limit on the boundary point, the estimations below of the modulus of angular derivative have been obtained.

• Korean Journal of Mathematics
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• v.27 no.4
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• pp.1027-1041
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• 2019

In this paper, we present a Schwarz lemma at the boundary for analytic functions at the unit disc, which generalizes classical Schwarz lemma for bounded analytic functions. For new inequalities, the results of Jack's lemma and Hankel determinant were used. We will get a sharp upper bound for Hankel determinant H₂(1). Also, in a class of analytic functions on the unit disc, assuming the existence of angular limit on the boundary point, the estimations below of the modulus of angular derivative have been obtained.

• Bulletin of the Korean Mathematical Society
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• v.35 no.3
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• pp.559-562
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• 1998

We prove the $C^r$ Closing Lemma for chain recurrence in compact surfaces.

• Honam Mathematical Journal
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• v.35 no.2
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• pp.163-171
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• 2013

By extending the negatively quadrant dependence, the paper puts forth the concept of extended negative quadrant dependence. A generalization of the second Borel-Cantelli lemma is obtained under extended negative quadrant dependence. Some applications are also introduced.

• Bulletin of the Korean Mathematical Society
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• v.37 no.4
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• pp.711-719
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• 2000

We generalize Gieseker\`s lemma and use it to compute Picard number of a complete intersection surface.

• Kyungpook Mathematical Journal
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• v.52 no.2
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• pp.149-153
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• 2012

We show that the above lemma and its well-known refinement are valid, in a general setting, in non-commutative rings. Some interesting consequences are also observed.

• Bulletin of the Korean Mathematical Society
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• v.49 no.2
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• pp.417-422
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• 2012

In this paper, we prove an analog of the generalized Schwarz lemma for meromorphic functions. Our results improve the classical generalized Schwarz lemma.