• 대한수학회지
• /
• 제41권1호
• /
• pp.175-192
• /
• 2004

This talk discusses conditions on the numerical range of a holomorphic function defined on a bounded convex domain in a complex Banach space that imply that the function has a unique fixed point. In particular, extensions of the Earle-Hamilton Theorem are given for such domains. The theorems are applied to obtain a quantitative version of the inverse function theorem for holomorphic functions and a distortion form of Cartan's unique-ness theorem.

• 대한수학회논문집
• /
• 제33권3호
• /
• pp.901-917
• /
• 2018

In this paper, we first introduce the notions of (2, ${\beta}$)-Banach spaces and we will reformulate the fixed point theorem [10, Theorem 1] in this space. We also show that this theorem is a very efficient and convenient tool for proving the new hyperstability results of the general linear equation in (2, ${\beta}$)-Banach spaces. Our main results state that, under some weak natural assumptions, functions satisfying the equation approximately (in some sense) must be actually solutions to it. Our results are improvements and generalizations of the main results of Piszczek [34], Brzdęk [6, 7] and Bahyrycz et al. [2] in (2, ${\beta}$)-Banach spaces.

• Journal of applied mathematics & informatics
• /
• 제4권2호
• /
• pp.573-581
• /
• 1997

In this paper we prove a weak common fixed point theo-rem in a normed almost linear space which is different from the result of S. P. Singh and B.A. Meade [9]. However for a Banach X our theorem is equal to the result of S. P. Singh and B. A. Meade.

• 대한수학회지
• /
• 제52권1호
• /
• pp.125-139
• /
• 2015

In this paper we introduce the notion of the generalized Darbo fixed point theorem and prove some fixed and coupled fixed point theorems in Banach space via the measure of non-compactness, which generalize the result of Aghajani et al. [6]. Our results generalize, extend, and unify several well-known comparable results in the literature. One of the applications of our main result is to prove the existence of solutions for the system of integral equations.

• Nonlinear Functional Analysis and Applications
• /
• 제26권5호
• /
• pp.1021-1034
• /
• 2021

This paper deals with a nonlinear Langevin equation involving two fractional orders with three-point boundary conditions. Our aim is to find the existence of solutions for the proposed Langevin equation by using the Banach contraction mapping principle and the Krasnoselskii's fixed point theorem. Three examples are also given to show the significance of our results.

• 대한수학회보
• /
• 제34권3호
• /
• pp.491-493
• /
• 1997

This is to clarify that Taskovic's extension of the Brouwer fixed point theorem is incorrectly stated.

• 충청수학회지
• /
• 제28권3호
• /
• pp.365-375
• /
• 2015

Of concern is the existence, uniqueness, and continuous dependence of a mild solution of a nonlocal Cauchy problem for a semilinear mixed Volterra-Fredholm functional integrodifferential equation. Our analysis is based on the theory of a strongly continuous semigroup of operators and the Banach fixed point theorem.

• Korean Journal of Mathematics
• /
• 제18권3호
• /
• pp.299-309
• /
• 2010

In this paper, we study the first order nonlinear neutral difference equation: $${\Delta}(x(n)+px(n-{\tau}))+f(n,x(n-c),x(n-d))=r(n),\;n{\geq}n_0$$. Using the Banach fixed point theorem, we prove the existence of bounded positive solutions of the equation, suggest Mann iterative schemes of bounded positive solutions, and discuss the error estimates between bounded positive solutions and sequences generated by Mann iterative schemes.

• 대한수학회보
• /
• 제46권4호
• /
• pp.691-700
• /
• 2009

We prove the local existence of classical solutions of quasi-linear integrodifferential equations in Banach spaces. The results are obtained by using fractional powers of operators and the Schauder fixed-point theorem. An example is provided to illustrate the theory.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• 제9권1호
• /
• pp.16-19
• /
• 2009

In this paper, we study the existence and uniqueness of solutions for the fuzzy differential equations in n-dimension fuzzy vector space $(E_N)^n$ using by Banach fixed point theorem.