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Using a Set to Construct a Group Topology
Ellen Clay ...et al KYUNGPOOK UNIVERSITY 1997 Kyungpook mathematical journal Vol.37 No.1
The usual topology on the real line can be constructed in a natural fashion from the set (-∞, 1). It along with its opposite set (-1, ∞) and translates of these sets forms a subbasis for the usual topology. Hence the coarsets group topology on the reals containing the set (-1, ∞) is the usual topology. Many group topologies can be generated in this fashion. This paper will consider which group topologies can be generated in this fashion and which sets may be used to generate the topology.
On Certain Subclasses of p-valent Starlike Functions
J. Patel ...et al KYUNGPOOK UNIVERSITY 1996 Kyungpook mathematical journal Vol.36 No.1
In the present paper, we introduce two subclasses T^(*)_(p) (α,β,γ, A, B) and C_(p)(α,β,γ, A, B) of p-valent starlike functions in the unit disc U = {z : |z|< 1}. We prove certain coefficient inequalities, distortion theorems and substantially more general distortion theorems involving fractional derivatives and fractional integrals of functions belonging to the classes T^(*)_(p) (α,β,γ, A, B) and C_(p) (α,β,A,B).The raddi of p-valent convexity for functions belonging to these subclasses is also determine
H. France-Jackson ...et al KYUNGPOOK UNIVERSITY 1996 Kyungpook mathematical journal Vol.36 No.1
Hereditary radicals containing the Baer lower radical are investigated.
Remarks on Semi-generalized Closed Sets and Generalized Semi-closed Sets
H. Maki ..et al. KYUNGPOOK UNIVERSITY 1996 Kyungpook mathematical journal Vol.36 No.1
In this paper we study the product of generalized semi-closed sets and prove a product theorem on GSO-compact spaces. A new class of topological spaces, that is T_ (gs)spaces, is introduced. The homeomorphic image of T_ (gs)spaces and relationships among T_(1/2)spaces, semi-T_(1/2)spaces and T_ (gs)space are investigated.
Some Integrals Involving Kampé de Fériet's Series and I-function
Deepak Jain ...et al KYUNGPOOK UNIVERSITY 1996 Kyungpook mathematical journal Vol.36 No.1
In the present paper some integrals involving Kampé de Fé eriet's series and I-function have been evaluated. Some integrals involve Jacobi polynomials also. These integrals can be used effectively in the solution of heat conduction equation under given boundary conditions.
On Certain Subclasses of n-fold Symmetric Analytic Functions
J. Patel KYUNGPOOK UNIVERSITY 1996 Kyungpook mathematical journal Vol.36 No.2
In this paper, we determine the coeffcient estimates and distortion theorems for thesubclass U^(λ)_(n)(A,B) and V^(λ)_(n)(A,B) of n-fold symmetric analytic functions in the unit disc. We also establish the radius of starlikeness of the class U^(0)_(n)(A, B).
On Convex and Starshaped Hulls
M. Beltagy ...et al KYUNGPOOK UNIVERSITY 2000 Kyungpook mathematical journal Vol.40 No.2
This paper deals with the two main geometric concepts, convexity as well as star-shapedness, of subsets of Euclidean spaces. The concept of starshaped hull is introduced and studied from the geometric point of view. Additional geometric properties of convex hulls are established. Interesting examples are given to illustrate the obtained results.
Exponential Decay of C¹-quadratic Lagrange Spline and its Applications
Choi ,Taeg-Young ...et al KYUNGPOOK UNIVERSITY 1996 Kyungpook mathematical journal Vol.36 No.2
The exponential decay of C¹-quadratic Lagrange spline is shown when an interpolation point is chosen in each knot interval. Using such an exponential decay phenomena, the convergence of such a spline interpolant is proved. Moreover, as an application of C¹- quadratic Lagrange spline, we state brie°y the preconditioning result on the quadratic collocation method.
P. Nasehpour ...et al KYUNGPOOK UNIVERSITY 2000 Kyungpook mathematical journal Vol.40 No.2
Let R be a commutative ring with non-zero identy and let M be an R-module. An ideal a of R is called an M-cancellation ideal if whenever aP = aQ for submodules P and Q of M, then P = Q. This notion is a generalization of the notion, cancellation ideal. We use M-cancellation ideals and a generalization of Dedekind-Mertens lemma to prove that for an R-module M with Z_(R)(M) = {0}, the following statements are equivalent : (i) Every non-zero finitely generated ideal of R is an M-cancellation ideal of R. (ii) For every f ∈ R[t] and g ∈ M[t], c(fg) = c(f)c(g).
Birgit Jacob KYUNGPOOK UNIVERSITY 2000 Kyungpook mathematical journal Vol.40 No.2
We point out that the main result Theorem3.7 as well as Lemma 3.6 in the mentioned paper are wrong. Corrected versions of this results are presented.