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CERTAIN FRACTIONAL INTEGRAL INEQUALITIES ASSOCIATED WITH PATHWAY FRACTIONAL INTEGRAL OPERATORS
Agarwal, Praveen,Choi, Junesang Korean Mathematical Society 2016 대한수학회보 Vol.53 No.1
During the past two decades or so, fractional integral inequalities have proved to be one of the most powerful and far-reaching tools for the development of many branches of pure and applied mathematics. Very recently, many authors have presented some generalized inequalities involving the fractional integral operators. Here, using the pathway fractional integral operator, we give some presumably new and potentially useful fractional integral inequalities whose special cases are shown to yield corresponding inequalities associated with Riemann-Liouville type fractional integral operators. Relevant connections of the results presented here with those earlier ones are also pointed out.
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REGULAR MAPS-COMBINATORIAL OBJECTS RELATING DIFFERENT FIELDS OF MATHEMATICS
Nedela, Roman Korean Mathematical Society 2001 대한수학회지 Vol.38 No.5
Regular maps and hypermaps are cellular decompositions of closed surfaces exhibiting the highest possible number of symmetries. The five Platonic solids present the most familar examples of regular maps. The gret dodecahedron, a 5-valent pentagonal regular map on the surface of genus 5 discovered by Kepler, is probably the first known non-spherical regular map. Modern history of regular maps goes back at least to Klein (1878) who described in [59] a regular map of type (3, 7) on the orientable surface of genus 3. In its early times, the study of regular maps was closely connected with group theory as one can see in Burnside’s famous monograph [19], and more recently in Coxeter’s and Moser’s book [25] (Chapter 8). The present-time interest in regular maps extends to their connection to Dyck\`s triangle groups, Riemann surfaces, algebraic curves, Galois groups and other areas, Many of these links are nicely surveyed in the recent papers of Jones [55] and Jones and Singerman [54]. The presented survey paper is based on the talk given by the author at the conference “Mathematics in the New Millenium”held in Seoul, October 2000. The idea was, on one hand side, to show the relationship of (regular) maps and hypermaps to the above mentioned fields of mathematics. On the other hand, we wanted to stress some ideas and results that are important for understanding of the nature of these interesting mathematical objects.
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Homma, Masaaki,Kim, Seon-Jeong,Yoo, Mi-Ja Korean Mathematical Society 2004 대한수학회보 Vol.41 No.1
In our previous paper (Bull. Korean Math. Soc. 37(2000), 493-505), we claimed a theorem on a certain subset of a projective space over a finite field (Theorem 3.1). Recently, however, Professor Kato pointed out that our proof does not work if the field consists of two elements. Here we give an alternative proof of the theorem for the exceptional case.
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ERRATUM TO "PARANORMAL CONTRACTIONS AND INVARIANT SUBSPACES"
Duggal, B.P.,Kubrusly, C.S.,Levan, N. Korean Mathematical Society 2004 대한수학회지 Vol.41 No.4
In our paper "Paranormal contractions and invariant subspaces" published in Journal of the Korean Mathematical Society, Volume 40 (2003), Number 6, pp.933-942, the statement to observation (1) on page 935 should read:(omitted)
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ON CERTAIN GENERALIZED q-INTEGRAL OPERATORS OF ANALYTIC FUNCTIONS
PUROHIT, SUNIL DUTT,SELVAKUMARAN, KUPPATHAI APPASAMY Korean Mathematical Society 2015 대한수학회보 Vol.52 No.6
In this article, we first consider a linear multiplier fractional q-differintegral operator and then use it to define new subclasses of p-valent analytic functions in the open unit disk U. An attempt has also been made to obtain two new q-integral operators and study their sufficient conditions on some classes of analytic functions. We also point out that the operators and classes presented here, being of general character, are easily reducible to yield many diverse new and known operators and function classes.
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SOME CURIOSITIES OF THE ALGEBRA OF BOUNDED DIRICHLET SERIES
Mortini, Raymond,Sasane, Amol Korean Mathematical Society 2016 대한수학회보 Vol.53 No.1
It is shown that the algebra $\mathfrak{H}^{\infty}$ of bounded Dirichlet series is not a coherent ring, and has infinite Bass stable rank. As corollaries of the latter result, it is derived that $\mathfrak{H}^{\infty}$ has infinite topological stable rank and infinite Krull dimension.
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CYCLIC BRANCHED COVERS OF ALTERNATING KNOTS AND L-SPACES
TERAGAITO, MASAKAZU Korean Mathematical Society 2015 대한수학회보 Vol.52 No.4
For any alternating knot, it is known that the double branched cover of the 3-sphere branched over the knot is an L-space. We show that the three-fold cyclic branched cover is also an L-space for any genus one alternating knot.
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PRODUCT-TYPE OPERATORS FROM WEIGHTED BERGMAN-ORLICZ SPACES TO WEIGHTED ZYGMUND SPACES
JIANG, ZHI-JIE Korean Mathematical Society 2015 대한수학회보 Vol.52 No.4
Let ${\mathbb{D}}=\{z{\in}{\mathbb{C}}:{\mid}z{\mid}<1\}$ be the open unit disk in the complex plane $\mathbb{C}$, ${\varphi}$ an analytic self-map of $\mathbb{D}$ and ${\psi}$ an analytic function in $\mathbb{D}$. Let D be the differentiation operator and $W_{{\varphi},{\psi}}$ the weighted composition operator. The boundedness and compactness of the product-type operator $W_{{\varphi},{\psi}}D$ from the weighted Bergman-Orlicz space to the weighted Zygmund space on $\mathbb{D}$ are characterized.
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NOTES ON A QUESTION RAISED BY E. CALABI
Euh, Yunhee,Sekigawa, Kouei Korean Mathematical Society 2016 대한수학회보 Vol.53 No.1
We show that any orthogonal almost complex structure on a warped product Riemannian manifold of an oriented closed surface with nonnegative Gaussian curvature and a round 4-sphere is never integrable. This provides a partial answer to a question raised by E. Calabi.
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ORIGIN-SYMMETRIC CONVEX BODIES WITH MINIMAL MAHLER VOLUME IN ℝ<sup>2</sup>
Lin, Youjiang,Leng, Gangsong Korean Mathematical Society 2014 대한수학회보 Vol.51 No.1
In this paper, a new proof of the following result is given: The product of the volumes of an origin-symmetric convex bodies K in $\mathbb{R}^2$ and of its polar body is minimal if and only if K is a parallelogram.
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