• Journal of applied mathematics & informatics
• /
• v.37 no.5_6
• /
• pp.329-339
• /
• 2019

The Banach spaces $m^p(\phi)$ and $n^p(\phi)$ are very important sequence spaces related to $l_p$, which were defined to fill the gaps between $l_p(1{\leq}p{\leq}{\infty})$. In this paper, we investigated the solubility of the infinite system of differential equations in $m^p(\phi)$ and $n^p(\phi)$ by proving related theorems. Moreover, one example has been included for the justification of the claim of this paper.

• Kyungpook Mathematical Journal
• /
• v.60 no.4
• /
• pp.767-779
• /
• 2020

This paper primarily discusses and proves the Hyers-Ulam stability of three types of polynomial equations: xn+a1x+a0 = 0, anxn+⋯+a1x+a0 = 0, and the infinite series equation: ${\sum\limits_{i=0}^{\infty}}\;a_ix^i=0$, in dislocated quasi-metric spaces under certain conditions by constructing contraction mappings and using fixed-point methods. We present an example to illustrate that the Hyers-Ulam stability of polynomial equations in dislocated quasi-metric spaces do not work when the constant term is not equal to zero.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.15 no.3
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.46 no.4
• /
• 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.

• Korean Journal of Mathematics
• /
• v.28 no.1
• /
• pp.17-30
• /
• 2020

In this paper, we firstly introduce the class of C^*-algebra valued symmetric spaces and utilize the same to prove our fixed point results. We furnish an example to highlight the utility of our main result. Finally, we apply our result to examine the existence and uniqueness of a solution for a system of Fredholm integral equations.

• Journal of applied mathematics & informatics
• /
• v.33 no.1_2
• /
• pp.45-60
• /
• 2015

This paper is concerned with the existence of mild solutions for partial neutral functional integrodifferential equations with infinite delay in Banach spaces. The results are obtained by using resolvent operators and Krasnoselski-Schaefer type fixed point theorem. An example is provided to illustrate the results.

• Journal of applied mathematics & informatics
• /
• v.29 no.3_4
• /
• pp.681-696
• /
• 2011

In this paper, we consider the existence of mild solutions for a certain class of nonlinear impulsive functional evolution integrodifferential equation with nonlocal conditions in Banach spaces. A sufficient condition is established by using Schaefer's fixed point theorem combined with an evolution system. An example is also given to illustrate our result.

• Bulletin of the Korean Mathematical Society
• /
• v.38 no.1
• /
• pp.71-79
• /
• 2001

The purpose of this paper is to prove new equilibrium existence theorems of social systems with coordination under general conditions on the preference correspondence in locally convex spaces, and we also give an example which the previous existence results on SSC do not work but our theorem can be applied.

• The Pure and Applied Mathematics
• /
• v.20 no.3
• /
• pp.159-180
• /
• 2013

We establish a common fixed point theorem for mappings under ${\phi}$-contractive conditions on intuitionistic fuzzy metric spaces. As an application of our result we study the existence and uniqueness of the solution to a nonlinear Fredholm integral equation. We also give an example to validate our result.

• Communications of the Korean Mathematical Society
• /
• v.27 no.2
• /
• pp.347-356
• /
• 2012

In this paper, we present a common fixed point theorem for multivalued maps on $M$-complete fuzzy metric spaces. Also, the single valued case and an illustrative example are given.