• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.893-907
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• 2015

The Hyers-Ulam-Rassias stability of the k-th partial ternary quadratic derivations is investigated in non-Archimedean Banach ternary algebras and non-Archimedean $C^*$-ternary algebras by using the fixed point theorem.

• Kyungpook Mathematical Journal
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• v.45 no.2
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• pp.281-292
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• 2005

In this paper a nonlinear alternative of Leray-Schauder type is proved in a Banach algebra involving three operators and it is further applied to a functional nonlinear integral equation of mixed type $$x(t)=k(t,x({\mu}(t)))+[f(t,x({\theta}(t)))]\(q(t)+{\int}_0{^{\sigma}^{(t)}}v(t,s)g(s,x({\eta}\(s)))ds\)$$ for proving the existence results in Banach algebras under generalized Lipschitz and $Carath{\acute{e}}odory$ conditions.

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1065-1092
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• 2018

This manuscript is involved with a category of second-order impulsive functional integro-differential equations with nonlocal conditions in Banach spaces. Sufficient conditions for existence and approximate controllability of mild solutions are acquired by making use of the theory of cosine family, Banach contraction principle and Leray-Schauder nonlinear alternative fixed point theorem. An illustration is additionally furnished to prove the attained principles.

• Journal of Korean Society of Transportation
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• v.28 no.5
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• pp.131-139
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• 2010

The transport mode choice problem is to determine which of the alternative transport modes connecting an origin and destination will be used by a traveler. Most of the research relating to transport mode choice have mainly been focused on modeling, properties, and applications of the model, but rarely were concerned with equilibrium among the modes. This paper proves the equilibrium among the modes by using a logit mode choice model, and then verifies it with the Korean Transport Database (KTDB). In order to obtain such an equilibrium, this paper also presents a solution algorithm based on the fixed point theorem. The algorithm was tested with an example and confirmed the equilibrium solution.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1265-1277
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• 2009

In this paper, we apply a new decomposition method for solving initial and boundary value problems, which is due to Noor and Noor [18]. The analytical results are calculated in terms of convergent series with easily computable components. The diagonal Pade approximants are applied to make the work more concise and for the better understanding of the solution behavior. The proposed technique is tested on boundary layer problem; Thomas-Fermi, Blasius and sixth-order singularly perturbed Boussinesq equations. Numerical results reveal the complete reliability of the suggested scheme. This new decomposition method can be viewed as an alternative of Adomian decomposition method and homotopy perturbation methods.