• Kyungpook Mathematical Journal
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• 제61권3호
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• pp.559-581
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• 2021

In this paper, we establish the existence of solutions and the approximate controllability for the semilinear neutral differential control system under natural assumptions such as the local Lipschitz continuity of nonlinear term. First, we deal with the regularity of solutions of the neutral control system using fractional powers of operators. We also consider the approximate controllability for the semilinear neutral control equation, with a control part in place of a forcing term, using conditions for the range of the controller without the inequality condition as in previous results.

• East Asian mathematical journal
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• 제27권1호
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• pp.35-49
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• 2011

In this paper, we study multi-step iterative algorithm with errors and give the necessary and sufficient condition to converge to com mon fixed points for a finite family of asymptotically quasi-nonexpansive type mappings in Banach spaces. Also we have proved a strong convergence theorem to converge to common fixed points for a finite family said mappings on a nonempty compact convex subset of a uniformly convex Banach spaces. Our results extend and improve the corresponding results of [2, 4, 7, 8, 9, 10, 12, 15, 20].

• East Asian mathematical journal
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• 제29권3호
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• pp.315-326
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• 2013

In this paper, a new monotonicity, $M({\cdot},{\cdot})$-monotonicity, is introduced in Banach spaces, and the resolvent operator of an $M({\cdot},{\cdot})$-monotone operator is proved to be single valued and Lipschitz continuous. By using the resolvent operator technique associated with $M({\cdot},{\cdot})$-monotone operators, we construct a proximal point algorithm for solving a class of variational inclusions. And we prove the convergence of the sequences generated by the proximal point algorithms in Banach spaces. The results in this paper extend and improve some known results in the literature.

• 대한수학회보
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• 제59권6호
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• pp.1471-1493
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• 2022

The goal of this paper is to establish the boundedness of bilinear Calderón-Zygmund operator BT and its commutator [b₁, b₂, BT] which is generated by b₁, b₂ ∈ BMO(ℝⁿ) (or ${\dot{\Lambda}}_{\alpha}$(ℝⁿ)) and the BT on generalized variable exponent Morrey spaces 𝓛^p(·),𝜑(ℝⁿ). Under assumption that the functions 𝜑₁ and 𝜑₂ satisfy certain conditions, the authors proved that the BT is bounded from product of spaces 𝓛^{p₁(·),𝜑₁}(ℝⁿ)×𝓛^{p₂(·),𝜑₂}(ℝⁿ) into space 𝓛^p(·),𝜑(ℝⁿ). Furthermore, the boundedness of commutator [b₁, b₂, BT] on spaces L^p(·)(ℝⁿ) and on spaces 𝓛^p(·),𝜑(ℝⁿ) is also established.

• 대한수학회지
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• 제49권6호
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• pp.1273-1299
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• 2012

We prove the global regularity of weak solutions to a conormal derivative boundary value problem for quasilinear elliptic equations in divergence form on Lipschitz domains under the controlled growth conditions on the low order terms. The leading coefficients are in the class of BMO functions with small mean oscillations.

• 대한수학회논문집
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• 제21권4호
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• pp.689-700
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• 2006

In this paper, we introduce a new class of generalized nonlinear multivalued mixed quasi-variational-like inequalities and prove the existence and uniqueness of solutions for the class of generalized nonlinear multivalued mixed quasi-variational-like inequalities in reflexive Banach spaces using Fan-KKM Theorem.

• 대한수학회논문집
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• 제25권2호
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• pp.313-325
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• 2010

General models for the relaxed proximal point algorithm using the notion of relative maximal accretiveness (RMA) are developed, and then the convergence analysis for these models in the context of solving a general class of nonlinear inclusion problems differs significantly than that of Rockafellar (1976), where the local Lipschitz continuity at zero is adopted instead. Moreover, our approach not only generalizes convergence results to real Banach space settings, but also provides a suitable alternative to other problems arising from other related fields.

• Journal of applied mathematics & informatics
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• 제30권1_2호
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• pp.173-181
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• 2012

In this paper, we study the control problems governed by the semilinear parabolic type equation in Hilbert spaces. Under the Lipschitz continuity condition of the nonlinear term, we can obtain the sufficient conditions for the approximate controllability of nonlinear functional equations with nonlinear monotone hemicontinuous and coercive operator. The existence, uniqueness and a variation of solutions of the system are also given.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제18권3호
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• pp.219-230
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• 2011

We determine the radius of convergence for some Newton{type methods (NTM) for approximating a locally unique solution of an equation in a Banach space setting. A comparison is given between the radii of (NTM) and Newton's method (NM). Numerical examples further validating the theoretical results are also provided in this study.

• 충청수학회지
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• 제22권2호
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• pp.245-250
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• 2009

We consider a code function from the unit interval which has a generalized dyadic expansion into a coding space which has an associated ultra metric. The code function is not a bi-Lipschitz map but a dimension-preserving map in the sense that the Hausdorff and packing dimensions of any subset in the unit interval and its image under the code function coincide respectively.