• Nonlinear Functional Analysis and Applications
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• 제28권2호
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• pp.497-520
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• 2023

Numerous problems in science and engineering defined by nonlinear functional equations can be solved by reducing them to an equivalent fixed point problem. Fixed point theory provides essential tools for solving problems arising in various branches of mathematical analysis, such as split feasibility problems, variational inequality problems, nonlinear optimization problems, equilibrium problems, complementarity problems, selection and matching problems, and problems of proving the existence of solution of integral and differential equations.The theory of fixed is known to find its applications in many fields of science and technology. For instance, the whole world has been profoundly impacted by the novel Coronavirus since 2019 and it is imperative to depict the spread of the coronavirus. Panda et al. [24] applied fractional derivatives to improve the 2019-nCoV/SARS-CoV-2 models, and by means of fixed point theory, existence and uniqueness of solutions of the models were proved. For more information on applications of fixed point theory to real life problems, authors should (see [6, 13, 24] and the references contained in).

• Journal of applied mathematics & informatics
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• 제25권1_2호
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• pp.255-267
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• 2007

In this work, by using Xu's inequality, Nalder's results, the notion of $(A,\;{\eta})-accretive$ mappings and the new resolvent operator technique associated with $(A,\;{\eta})-accretive$ mappings due to Lan et al., we study the existence of solutions for a new class of $(A,\;{\eta})-accretive$ variational inclusion problems with non-accretive set-valued mappings and the convergence of the iterative sequences generated by the algorithms in Banach spaces. Our results are new and extend, improve and unify the corresponding results in this field.

• 충청수학회지
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• 제25권4호
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• pp.703-709
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• 2012

Recently, Kazmi and Khan [7] introduced a kind of equilibrium problem called generalized system (GS) with a single-valued bi-operator F. Next, in [10], the first author considered a generalization of (GS) into a multi-valued circumstance called the multi-valued quasi-generalized system (in short, MQGS). In the current work, we provide an extension of (MQGS) into a system of (MQGS) in general settings. This system is called the generalized multi-valued quasi-generalized system (in short, GMQGS). Using the existence theorem for abstract economy by Kim [8], we prove the existence of solutions for (GMQGS) in the framework of Hausdorff topological vector spaces. As an application, an existence result of a system of generalized vector quasi-variational inequalities is derived.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제16권2호
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• pp.199-212
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• 2009

We investigate the multiplicity of the nontrivial periodic solutions for a class of the system of the nonlinear suspension bridge equations with Dirichlet boundary condition and periodic condition. We show that the system has at least two nontrivial periodic solutions by the abstract version of the critical point theory on the manifold with boundary. We investigate the geometry of the sublevel sets of the corresponding functional of the system and the topology of the sublevel sets. Since the functional is strongly indefinite, we use the notion of the suitable version of the Palais-Smale condition.

• 대한교통학회지
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• 제20권1호
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• pp.77-90
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• 2002

네트웤확장은 평형통행배정모형에서 교차로의 지체와 같이 방향별로 발생하는 교차로의 움직임을 고려하기위한 필수불가결한 방법으로 사용되어져 왔다. 그러나 이 방법은 교차로에서 발생하는 가능한 방향별움직임을 가상 링크를 추가하여 표현함으로 네트웤의 복잡성이 증가하고 계산노력이 많이 요구되어진다. 본 연구에서는 이러한 방향별지체와 이에 관련된 움직임을 네트웤의 구조를 확장함이 없이 이용가능한 사용자최적통행배정모형을 새로운 변동부등식를 통해 제안한다. 제안된 식에 회전지체함수가 직접적으로 내재되므로 네트웤의 어떤 변화도 요구되지 않으며 교차로의 방향별움직임에서 나타나는 상호연관성이 변동부등식의 특성을 통해 명쾌하게 반영된다. 제안된 변동부등식의 해법으로서 변형된 대 각화알고리즘이 제안되며 이때 링크표지덩굴망알고리즘이 각 교차로에서 발생하는 방향별지체를 고려하여 최적경로를 발견하는데 응용된다. 제안된 모델을 통한 실험결과로서 자용자최적평형조건이 만족됨이 확인되었으며 교차로주변에서 회전금지와 함께 목격되는 유턴, 피턴과 같이 두번 이상 같은 교차로를 통과하는 통행행태가 운전자의 경로파악시 발생됨을 확인되었다. 본 연구에서 제안된 모델은 네트웤의 교차로의 움직임을 파악하기위해 구축하는데 요구되는 노력을 감축하고, 컴퓨터계산노력을 절감하며, 향후 첨단여행정보시스템을 구축하는데 기여할 것으로 기대된다.

• 대한수학회보
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• 제41권3호
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• pp.435-450
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• 2004

We show that two concepts of h-stability and h-stability in variation for nonlinear difference systems are equivalent by using the concept of $n_{\infty}$-summable similarity of their associated variational systems. Also, we study h-stability for perturbed non-linear system y(n+1) =f(n,y(n)) + g(n,y(n), Sy(n)) of nonlinear difference system x(n+1) =f(n,x(n)) using the comparison principle and extended discrete Bihari-type inequality.

• Journal of applied mathematics & informatics
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• 제7권1호
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• pp.1-28
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• 2000

In the present paper, we introduce fundamental results in the KKM theory for G-convex spaces which are equivalent to the Brouwer theorem, the Sperner lemma, and the KKM theorem. Those results are all abstract versions of known corresponding ones for convex subsets of topological vector spaces. Some earlier applications of those results are indicated. Finally, We give a new proof of the Himmelberg fixed point theorem and G-convex space versions of the von Neumann type minimax theorem and the Nash equilibrium theorem as typical examples of applications of our theory.

• 한국소음진동공학회논문집
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• 제13권3호
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• pp.172-179
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• 2003

Linear matrix Inequality based $H_\infty$ robust controller is designed to control the motion of a 4-axis unbalanced rigid asymmetric rotor supported and controlled by two active magnetic bearings in this paper. To this end, the equations of motion of the system are derived via Hamilton's variational principle and transformed to a state-space form for the standard $H_\infty$ control problem. LMI-based controller, which does not require additional assumptions beyond the usual stabilizability and detectability assumptions, is designed based upon the pole place weighting function and loopshaping technique. The obtained results are compared with those reported in the available literature and the efficiency of the proposed LMI-based $H_\infty$ control is revealed.

• East Asian mathematical journal
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• 제17권1호
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• pp.57-70
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• 2001

In this paper, we introduce a class of generalized quasivariational inclusions for fuzzy mappings and show its equivalence with a class of fixed point problems. Using this equivalence, we develop the Mann and Ishikawa type perturbed iterative algorithms for this class of generalized quasivariational inclusions. Further, we prove the existence of solutions for the class of generalized quasivariational inclusions and discuss the convergence criteria for the perturbed algorithms.

• Journal of applied mathematics & informatics
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• 제30권3_4호
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• pp.613-622
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• 2012

In this paper, we propose a new algorithm to modify the standard Mann' process to have strong convergence for $k$-strictly pseudo-contractive non-self mapping in Hilbert spaces.