• Korean Journal of Mathematics
• /
• v.31 no.3
• /
• pp.323-337
• /
• 2023

In this paper, we have defined bicomplex valued functions of bounded variations and rectifiable hyperbolic path. We have studied the integration of product-type bicomplex valued functions on rectifiable hyperbolic path. Also we have established bicomplex analogue of the Fundamental Theorem of Calculus for hyperbolic line integral.

• Korean Journal of Mathematics
• /
• v.24 no.4
• /
• pp.647-662
• /
• 2016

In this paper, we study Lipschitz continuous, the boundedness and compactness of the composition operator $C_{\phi}$ acting between the general hyperbolic Bloch type-classes ${\mathcal{B}}^{\ast}_{p,{\log},{\alpha}}$ and general hyperbolic Besov-type classes $F^{\ast}_{p,{\log}}(p,q,s)$. Moreover, these classes are shown to be complete metric spaces with respect to the corresponding metrics.

• Korean Journal of Mathematics
• /
• v.31 no.2
• /
• pp.189-201
• /
• 2023

In this article, we establish Hilbert-type integral inequalities with the help of a non-homogeneous kernel of hyperbolic function with best constant factor. We also study the obtained inequalities's equivalent form. Additionaly, several specific Hilbert's type inequalities with constant factors in the term of the rational fraction expansion of higher order derivatives of cotangent and cosine functions are presented.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.25 no.4
• /
• pp.173-195
• /
• 2021

A new implicit discontinuous Galerkin spectral element method (DGSEM) based on the first order hyperbolic system(FOHS) is presented for solving elliptic type partial different equations, such as the Poisson problems. By utilizing the idea of hyperbolic formulation of Nishikawa[1], the original Poisson equation was reformulated in the first-order hyperbolic system. Such hyperbolic system is solved implicitly by the collocation type DGSEM. The steady state solution in pseudo-time, which is the solution of the original Poisson problem, was obtained by the implicit solution of the global linear system. The optimal polynomial orders of 𝒪(𝒽^𝑝+1)) are obtained for both the solution and gradient variables from the test cases in 1D and 2D regular grids. Spectral accuracy of the solution and gradient variables are confirmed from all test cases of using the uniform grids in 2D.

• Communications of the Korean Mathematical Society
• /
• v.37 no.4
• /
• pp.1249-1258
• /
• 2022

In this study, we show that the strong exponential limit shadowing property (SELmSP, for short), which has been recently introduced, exists on a neighborhood of a hyperbolic set of a diffeomorphism. We also prove that Ω-stable diffeomorphisms and 𝓛-hyperbolic homeomorphisms have this type of shadowing property. By giving examples, it is shown that this type of shadowing is different from the other shadowings, and the chain transitivity and chain mixing are not necessary for it. Furthermore, we extend this type of shadowing property to positively expansive maps with the shadowing property.

• Honam Mathematical Journal
• /
• v.42 no.2
• /
• pp.301-318
• /
• 2020

In this paper, we introduce and study the concept of hyperbolic type convexity functions and their some algebraic properties. We obtain Hermite-Hadamard type inequalities for this class of functions. In addition, we obtain some refinements of the Hermite-Hadamard inequality for functions whose first derivative in absolute value, raised to a certain power which is greater than one, respectively at least one, is hyperbolic convexity. Moreover, we compare the results obtained with both Hölder, Hölder-İşcan inequalities and power-mean, improved-power-mean integral inequalities.

• East Asian mathematical journal
• /
• v.15 no.2
• /
• pp.325-336
• /
• 1999

In this paper, we prove that any $\lambda$-firmly nonexpansive mapping ($0<\lambda<1)T:C{\rightarrow}C$ has a fixed point in C whenever C is a finite union of nonempty, bounded, closed and convex subsets of a metric space of hyperbolic type.

• Communications of the Korean Mathematical Society
• /
• v.13 no.1
• /
• pp.171-179
• /
• 1998

In this paper, we establish Trotted-Kato type convergence theoren for nonlinear semigroups generated by coaccretive operators in a hyperbolic space.

• East Asian mathematical journal
• /
• v.14 no.1
• /
• pp.205-217
• /
• 1998

We obtain some theorems on nonexistence of certain finite type closed curves on the pseudo-hyperbolic space $H^4(-c^2)$ in the Minkowski spacetime $E^5_1$.

• Journal of the Korean Mathematical Society
• /
• v.60 no.3
• /
• pp.619-634
• /
• 2023

This paper considers a parabolic-hyperbolic-hyperbolic type chemotaxis system in ℝ^d, d ≥ 3, describing tumor-induced angiogenesis. The global existence result and temporal decay estimate for a unique mild solution are established under the assumption that some Sobolev norms of initial data are sufficiently small.