• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.1005-1013
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• 2014

Let ${\phi}$ be an analytic self map of the open unit disc D. In this paper, we study the composition operator $C_{\phi}$ from the Bergman space on D to the Hardy space on D.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.901-910
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• 2008

For some generalized N-function ${\Phi}$, some Holder type inequalities and bounded operators on spaces of type $W_M^{\Omega,\Phi}$ generalizing the $W^p$-spaces due to Pathak and Upadhyay are obtained.

• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.421-432
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• 2005

Suppose that an infinite graph G of bounded degree has finite number of ends, each of which is p-regular, where $1. Then we can identify all the positive (bounded, respectively) p-harmonic functions on G.

• Korean Journal of Mathematics
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• v.16 no.4
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• pp.499-509
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• 2008

In this paper we introduce the concepts of the generalized bounded variation in the restricted sense with respect to a strictly increasing function and $Denjoy_*$-Stieltjes integral of real-valued functions and investigate their properties.

• Kyungpook Mathematical Journal
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• v.45 no.4
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• pp.571-577
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• 2005

The aim of this paper is to establish the rate of convergence of Baskakov-Durrmeyer operators for bounded variation function. We have given the better estimate over the results due to Guo ([4]), Anial and Teberska ([1]) and Gupta and Srivastava ([8]).

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

• Bulletin of the Korean Mathematical Society
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• v.37 no.4
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• pp.743-753
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• 2000

In the space $C_1(X)$ of real-valued continuous functions with $L_1-norm$, every bounded set has a relative Chebyshev center in a finite-dimensional subspace S. Moreover, the set function $F\rightarrowZ_S(F)$ corresponding to F the set of its relative Chebyshev centers, in continuous on the space B[$C_1(X)$(X)] of nonempty bounded subsets of $C_1(X)$ (X) with the Hausdorff metric. In particular, every bounded set has a relative Chebyshev center in the closed convex set S(F) of S and the set function $F\rightarrowZ_S(F)$(F) is continuous on B[$C_1(X)$ (X)] with a condition that the sets S(.) are equal.

• Journal of the Korean Mathematical Society
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• v.45 no.3
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• pp.807-819
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• 2008

We prove that for any continuous function f on the s-harmonic (1{\infty})$ boundary of a complete Riemannian manifold M, there exists a solution, which is a limit of a sequence of bounded energy finite solutions in the sense of supremum norm, for a certain elliptic operator A on M whose boundary value at each s-harmonic boundary point coincides with that of f. If $E_1,\;E_2,...,E_{\iota}$ are s-nonparabolic ends of M, then we also prove that there is a one to one correspondence between the set of bounded energy finite solutions for A on M and the Cartesian product of the sets of bounded energy finite solutions for A on $E_i$ which vanish at the boundary ${\partial}E_{\iota}\;for\;{\iota}=1,2,...,{\iota}$

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.12
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• pp.2926-2934
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• 2000

This study presents a direct adaptive controller which is derived by using Lyapunovs direct methods for trajectory tracking control of a pneumatic cylinder. The structure of the controller is very simple and computationally efficient because it does not use either the dynamic model or the parameter values of the pneumatic system. The bounded stability of the system is shown in the presence of the bounded unmodeled dynamics. The bounded size of tracking errors can be made arbitrarily small without giving andy influences on either input or output variables. The trajectory tracking performance and the stability of the control system is verified experimentally. The results of the experiments show that the proposed controller tracks the given trajectories, sine function and cycloidal function trajectories, more accurately than PD controller does, and it stabilizes the system and adaptive variables.

• Communications of the Korean Mathematical Society
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• v.22 no.2
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• pp.277-287
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• 2007

We prove that if a graph G of bounded degree has finitely many p-hyperbolic ends($1) in which every bounded energy finite p-harmonic function is asymptotically constant for almost every path, then the set $\mathcal{HBD}_p(G)$ of all bounded energy finite p-harmonic functions on G is in one to one corresponding to $\mathbf{R}^l$, where $l$ is the number of p-hyperbolic ends of G. Furthermore, we prove that if a graph G' is roughly isometric to G, then $\mathcal{HBD}_p(G')$ is also in an one to one correspondence with $\mathbf{R}^l$.