• 대한수학회논문집
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• 제9권2호
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• pp.303-315
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• 1994

Let X be a real Banach space with norm ∥ㆍ∥. Let T > 0, r ≥a be fixed constants. We denote by L/sup p/ the usual L/sup p/( -r, 0; X) with norm ∥ㆍ∥/sub p/ for 1 ≤p < ∞. Our object is to study the existence of solutions of nonlinear functional evolution equations of the type (FDE) x'(t) ＋ A(t)x(t) = G(t, x/sub t/), 0 ≤t ≤T, x/sub 0/ = ø.(omitted)

• Nonlinear Functional Analysis and Applications
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• 제27권3호
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• pp.449-469
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• 2022

This paper deals with the new iterative algorithm for approximating the fixed point of generalized 𝛼-nonexpansive mappings in a hyperbolic space. We show that the proposed iterative algorithm is faster than all of Picard, Mann, Ishikawa, Noor, Agarwal, Abbas, Thakur and Piri iteration processes for contractive mappings in a Banach space. We also establish some weak and strong convergence theorems for generalized 𝛼-nonexpansive mappings in hyperbolic space. The examples and numerical results are provided in this paper for supporting our main results.

• 대한수학회보
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• 제36권4호
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• pp.629-636
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• 1999

We introduce Lipschitz algebras of differentiable functions of a perfect compact plane set X and extend the definition to Lipschitz algebras of infinitely differentiable functions of X. Then we define the subalgebras generated by polynomials, rational functions, and analytic functions in some neighbourhood of X, and determine the maximal ideal spaces of some of these algebras. We investigate the polynomial and rational approximation problems on certain compact sets X.

• 대한수학회보
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• 제42권4호
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• pp.757-776
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• 2005

In this paper we establish the stability of a Jensen type functional equation, namely f(xy) - f($xy^{-1}$) = 2f(y), on some classes of groups. We prove that any group A can be embedded into some group G such that the Jensen type functional equation is stable on G. We also prove that the Jensen type functional equation is stable on any metabelian group, GL(n, $\mathbb{C}$), SL(n, $\mathbb{C}$), and T(n, $\mathbb{C}$).