• The Pure and Applied Mathematics
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• v.27 no.1
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• pp.25-33
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• 2020

In this paper, we consider the following quadratic (ρ₁, ρ₂)-functional equation (0, 1) $$N(2f({\frac{x+y}{2}})+2f({\frac{x-y}{2}})-f(x)-f(y)-{\rho}_1(f(x+y)+f(x-y)-2f(x)-2f(y))-{\rho}_2(4f({\frac{x+y}{2}})+f(x-y)-f(x)-f(y)),t){\geq}{\frac{t}{t+{\varphi}(x,y)}}$$, where ρ₂ are fixed nonzero real numbers with ρ₂ ≠ 1 and 2ρ₁ + 2ρ₂≠ 1, in fuzzy normed spaces. Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic (ρ₁, ρ₂)-functional equation (0.1) in fuzzy Banach spaces.

• The Pure and Applied Mathematics
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• v.24 no.1
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• pp.21-31
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• 2017

In this paper, we introduce and solve the following additive (${\rho}_1$, ${\rho}_2$)-functional inequality $${\Large{\parallel}}2f(\frac{x+y}{2})-f(x)-f(y){\Large{\parallel}}{\leq}{\parallel}{\rho}_1(f(x+y)+f(x-y)-2f(x)){\parallel}+{\parallel}{\rho}_2(f(x+y)-f(x)-f(y)){\parallel}$$ where ${\rho}_1$ and ${\rho}_2$ are fixed nonzero complex numbers with $\sqrt{2}{\mid}{\rho}_1{\mid}+{\mid}{\rho}_2{\mid}<1$. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive (${\rho}_1$, ${\rho}_2$)-functional inequality (1) in complex Banach spaces.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.3
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• pp.365-375
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• 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.

• East Asian mathematical journal
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• v.28 no.5
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• pp.533-541
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• 2012

A common fixed point result of Gregus type for subcompatible mappings defined on a complete linear metric space is obtained. The considered underlying space is generalized from Banach space to complete linear metric spaces, which include Banach space and complete metrizable locally convex spaces. Invariant approximation results have also been determined as its application.

• Journal of applied mathematics & informatics
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• v.34 no.5_6
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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 applied mathematics & informatics
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• v.26 no.1_2
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• pp.325-336
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• 2008

In this paper, we prove the weak and strong convergence of the three-step iterative scheme with errors to a common fixed point for two asymptotically nonexpansive mappings in a uniformly convex Banach space under a condition weaker than compactness. Our theorems improve and generalize some previous results.

• Korean Journal of Mathematics
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• v.18 no.3
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• pp.299-309
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• 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.

• Bulletin of the Korean Mathematical Society
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• v.46 no.4
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• pp.691-700
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• 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.

• Bulletin of the Korean Mathematical Society
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• v.39 no.4
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• pp.561-569
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• 2002

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

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