• Journal of applied mathematics & informatics
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• 제34권5_6호
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• pp.509-517
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• 2016

In this paper, we consider the following functional equation with involution f(x + y) + f(x + σ(y)) = 2f(x) + f(y) + f(σ(y)) and prove the generalized Hyers-Ulam stability for it when the target space is a non-Archimedean Banach space.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제15권3호
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• pp.177-190
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• 2011

According to fractional calculus theory and Banach's fixed point theorem, we establish the sufficient conditions for the controllability of impulsive fractional evolution integrodifferential equations in Banach spaces. An example is provided to illustrate the theory.

• 대한수학회보
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• 제52권2호
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• pp.685-697
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• 2015

We investigate the stability of nonlinear differential equations of the form $y^{(n)}(x)=F(x,y(x),y^{\prime}(x),{\cdots},y^{(n-1)}(x))$ with a Lipschitz condition by using a fixed point method. Moreover, a Hyers-Ulam constant of this differential equation is obtained.

• 대한수학회논문집
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• 제23권3호
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• pp.427-446
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• 2008

In this paper, we give some new definitions of compatible mappings in intuitionistic fuzzy metric spaces and we prove a common fixed point theorem for four mappings under the condition of compatible mappings of type (I) and of type (II) in complete intuitionistic fuzzy metric spaces.

• Kyungpook Mathematical Journal
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• 제55권4호
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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.

• East Asian mathematical journal
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• 제24권1호
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• pp.111-123
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• 2008

In this paper, we introduce a new system of first-order impulsive fuzzy differential equations. By using Banach fixed point theorem, we obtain some new existence and uniqueness theorems of solutions for this system of first-order impulsive fuzzy differential equations in the metric space of normal fuzzy convex sets with distance given by maximum of the Hausdorff distance between level sets.

• 충청수학회지
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• 제28권2호
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• pp.173-186
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• 2015

In this paper, we consider a discrete fractional nonlinear boundary value problem in which nonlinear term f is involved with the fractional order difference. We transform the fractional boundary value problem into boundary value problem of integer order difference equation. By using a generalization of Leggett-Williams fixed-point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of at least three positive solutions.

• 충청수학회지
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• 제28권2호
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• pp.345-352
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• 2015

We study the existence of mild solutions of partial neutral integrodifferential equations with unbounded delay by using the fixed point criterion for condensing operators.

• 충청수학회지
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• 제29권2호
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• pp.187-220
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• 2016

This paper is concerned with a kind of non-homogeneous boundary value problems for singular second order differential systems with Laplacian operators. Using multiple fixed point theorems, sufficient conditions to guarantee the existence of at least three solutions of this kind of boundary value problems are established. An example is presented to illustrate the main results.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제11권1호
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• pp.85-93
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• 2007

In this paper we prove the existence of mild solutions of a first order impulsive initial value problems for functional differential equations in Banach spaces. The results are obtained by using the Lerey-Schauder nonlinear alternative fixed point theorem.