• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제8권1호
• /
• pp.41-54
• /
• 2004

Sufficient conditions for the controllability of neutral functional integrodifferential systems with infinite delay in Banach space are established by means of the Schaefer fixed point theorem.

• 대한수학회보
• /
• 제38권1호
• /
• pp.175-182
• /
• 2001

In this paper we prove the existence and uniqueness of a mild solution of a functional differential equation with nonlocal condition using the semigroup theory and the Banach fixed point principle.

• Korean Journal of Mathematics
• /
• 제26권4호
• /
• pp.809-822
• /
• 2018

In this paper, we introduce complex valued dislocated metric spaces. We prove Banach contraction principle, Kannan and Chatterjea type fixed point theorems in this new space. Moreover, we give some applications of the results to differential equations and iterated functions.

• Korean Journal of Mathematics
• /
• 제31권1호
• /
• pp.121-122
• /
• 2023

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제19권4호
• /
• pp.397-407
• /
• 2012

Let X and Y be vector spaces. We introduce a new type of a cubic functional equation $f$ : $X{\rightarrow}Y$. Furthermore, we assume X is a vector space and (Y, N) is a fuzzy Banach space and then investigate a fuzzy version of the generalized Hyers-Ulam stability in fuzzy Banach space by using fixed point method for the cubic functional equation.

• 대한수학회보
• /
• 제48권3호
• /
• pp.491-503
• /
• 2011

Using the fixed point method, we prove the generalized Hyers-Ulam stability of the following cubic-quartic functional equation (0.1) f(2x + y) + f(2x - y) = 3f(x + y) + f(-x - y) + 3f(x - y) + f(y - x) + 18f(x) + 6f(-x) - 3f(y) - 3f(-y) in fuzzy Banach spaces.

• Korean Journal of Mathematics
• /
• 제17권3호
• /
• pp.315-330
• /
• 2009

Using the fixed point method, we prove the generalized Hyers-Ulam stability of the following cubic-quadratic functional equation $$(0.1)\;\frac{1}{2}(f(2x+y)+f(2x-y)-f(-2x-y)-f(y- 2x))\\{\hspace{35}}=2f(x+y)+2f(x-y)+4f(x)-8f(-x)-2f(y)-2f(-y)$$ in fuzzy Banach spaces.

• 충청수학회지
• /
• 제31권2호
• /
• pp.199-230
• /
• 2018

In this paper, we introduce the general form of a viginti functional equation. Then, we find the general solution and study the generalized Ulam-Hyers stability of such functional equation in multi-Banach spaces by using fixed point technique. Also, we indicate an example for non-stability case regarding to this new functional equation.

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

• 대한수학회지
• /
• 제54권2호
• /
• pp.493-506
• /
• 2017

In this paper, we define the modulus of n-dimensional U-flatness as the determinant of an $(n+1){\times}(n+1)$ matrix. The properties of the modulus are investigated and the relationships between this modulus and other geometric parameters of Banach spaces are studied. Some results on fixed point theory for non-expansive mappings and normal structure in Banach spaces are obtained.