• Bulletin of the Korean Mathematical Society
• /
• v.38 no.1
• /
• pp.113-120
• /
• 2001

Using the notions of admissibility, local convexity and measure of noncompactness, we give new fixed point theorems for quasicompact or condensing multivalued mappings with domains that are not necessarily convex subsets of an arbitrary topological vector space.

• Journal of the Korean Mathematical Society
• /
• v.55 no.4
• /
• pp.877-895
• /
• 2018

In this paper, we show that an unbounded $S_0$-demicompact linear operator T with respect to a bounded linear operator $S_0$, acting on a Banach space, can be characterized by the Kuratowskii measure of noncompactness. Moreover, some other quantities related to this measure provide sufficient conditions to the operator T to be $S_0$-demicompact. The obtained results are used to discuss the connection with Fredholm and upper Semi-Fredholm operators.

• The Pure and Applied Mathematics
• /
• v.27 no.1
• /
• pp.13-24
• /
• 2020

In this article, we investigate the solvability of nonlinear fractional integro-differential equations of the Hammerstein type. The results are obtained using the technique of measure of noncompactness and the Darbo theorem in the real Banach space of continuous and bounded functions in the interval [0, a]. At the end, an example is presented to illustrate the effectiveness of the obtained results.

• Journal of applied mathematics & informatics
• /
• v.42 no.2
• /
• pp.399-415
• /
• 2024

We looked at nonlocal controllability for Hilfer fractional differential equations with almost sectorial operator in this manuscript. We show certain necessary criteria for nonlocal controllability using the measure of noncompactness and the Mönch fixed point theorem. Finally, we provided theoretical and practical applications are given to demonstrate how the abstract results might be applied.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.16 no.2
• /
• pp.93-105
• /
• 2012

In this paper, we consider the controllability of a certain class of impulsive neutral evolution differential equations in Banach spaces. Sufficient conditions for controllability are obtained by using the Hausdorff measure of noncompactness and Monch fixed point theorem under the assumption of noncompactness of the evolution system.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.15 no.4
• /
• pp.253-265
• /
• 2011

In this paper, we study the existence of mild solutions for double perturbed impulsive neutral functional evolution equations with infinite delay in Banach spaces. The existence of mild solutions to such equations is obtained by using the theory of the Hausdorff measure of noncompactness and Darbo fixed point theorem, without the compactness assumption on associated evolution system. An example is provided to illustrate the theory.

• Journal of the Korean Mathematical Society
• /
• v.51 no.6
• /
• pp.1123-1139
• /
• 2014

In this work, we investigate the existence of the extremal solutions for a class of fractional partial differential equations with order 1 < ${\alpha}$ < 2 by upper and lower solution method. Using the theory of Hausdorff measure of noncompactness, a series of results about the solutions to such differential equations is obtained.

• Korean Journal of Mathematics
• /
• v.27 no.4
• /
• pp.949-968
• /
• 2019

In this work, we characterize some matrix classes concerning the Binomial sequence spaces b^r,s_∞ and b^r,s_p, where 1 ≤ p < ∞. Moreover, by using the notion of Hausdorff measure of noncompactness, we characterize the class of compact matrix operators from b^r,s₀, b^r,s_c and b^r,s_∞ into c₀, c and ℓ_∞, respectively.

• Journal of the Korean Mathematical Society
• /
• v.36 no.4
• /
• pp.829-832
• /
• 1999

This to correct Section 4 of our previous work [1].

• Nonlinear Functional Analysis and Applications
• /
• v.28 no.1
• /
• pp.57-79
• /
• 2023

We investigate the existence and uniform attractivity of solutions of a class of functional integral equations which contain a number of classical nonlinear integral equations as special cases. Using the technique of measures of noncompactness and a fixed point theorem of Darbo type we prove the existence of solutions of these equations in the Banach space of continuous and bounded functions on the nonnegative real half axis. Our results extend and improve some known results in the recent literature. An example illustrating the main result is presented in the last section.