scholarly journals Ulam’s type stability of Hadamard type fractional integral equations

Filomat ◽  
2014 ◽  
Vol 28 (7) ◽  
pp. 1323-1331 ◽  
Author(s):  
Jinrong Wang ◽  
Zeng Lin
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fractional Integral ◽  
Fixed Point Method ◽  
Point Method ◽  
Singular Kernel ◽  
Compact Interval ◽  
Ulam’S Type Stability ◽  
Stability Results

In this paper, we further investigates Ulam?s type stability of Hadamard type fractional integral equations on a compact interval. We explore new conditions and develop valuable techniques to overcome the difficult from the Hadamard type singular kernel and extend the previous Ulam?s type stability results in [27] from [1, b] to [a, b] with a > 0 via fixed point method. Finally, two examples are given to illustrate our results.

scholarly journals On a New Stability Problem of Radical nth-Degree Functional Equation by Brzdęk’s Fixed-Point Method

2019 ◽  
Vol 2019 ◽  
pp. 1-6
Author(s):  
Dongseung Kang ◽  
Hoewoon B. Kim
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Positive Integer ◽  
Stability Problem ◽  
Fixed Point Method ◽  
Point Method ◽  
General Solutions ◽  
Ulam Type Stability ◽  
Stability Results

In this paper, we introduce the radical nth-degree functional equation of the form f(xn+ynn)=f(x)+f(y) with a positive integer n, discuss its general solutions, and prove new Hyers-Ulam-type stability results for the equation by using Brzdęk’s fixed-point method.

scholarly journals A general fixed point method for the stability of the monomial functional equation

2012 ◽  
Vol 28 (1) ◽  
pp. 25-36
Author(s):  
LIVIU CADARIU ◽  
◽  
VIOREL RADU ◽  
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Method ◽  
Point Method ◽  
Normed Spaces ◽  
Jensen Functional Equation ◽  
Jensen Functional ◽  
Error Estimations ◽  
The Stability ◽  
Stability Results

In this paper, we extend the ideas in [Cadariu, L. and Radu, V., ˘ A general fixed point method for the stability of Jensen functional equation, Bull. S¸ t. Univ. Politehnica Timis¸oara, Ser. Mat.-Fiz. 51(65) (2006), No. 2, 63–72] to obtain some general stability results for monomial functional equations in β−normed spaces. The fixed point alternative together the error estimations for generalized contractions of type Bianchini-Grandolfi are pointed out, and then used as fundamental tool. Some applications and examples which emphasize the very general hypotheses, are also given.

scholarly journals Fixed point method and its improvement for the system of Volterra-Fredholm integral equations of the second kind

MATEMATIKA ◽  
2017 ◽  
Vol 33 (2) ◽  
pp. 191
Author(s):  
Talaat Ismahel Hasan ◽  
Shaharuddin Salleh
Keyword(s):  
Fixed Point ◽  
Exact Solutions ◽  
Integral Equations ◽  
Fixed Point Method ◽  
Point Method ◽  
Fredholm Integral Equations ◽  
Numerical Examples ◽  
New Algorithms

In this paper, we consider the system of Volterra-Fredholm integral equations of the second kind (SVFI-2). We proposed fixed point method (FPM) to solve SVFI-2 and improved fixed point method (IFPM) for solving the problem. In addition, a few theorems and two new algorithms are introduced.  They are supported by numerical examples and simulations using Matlab. The results are reasonably good when compared with the exact solutions.

A fixed point approach to the stability of sextic Lie *-derivations

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4933-4944
Author(s):  
Dongseung Kang ◽  
Heejeong Koh
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
General Solution ◽  
Single Case ◽  
Fixed Point Method ◽  
Point Method ◽  
Fixed Point Approach ◽  
The Stability ◽  
The Given ◽  
Lie Derivations

We obtain a general solution of the sextic functional equation f (ax+by)+ f (ax-by)+ f (bx+ay)+ f (bx-ay) = (ab)2(a2 + b2)[f(x+y)+f(x-y)] + 2(a2-b2)(a4-b4)[f(x)+f(y)] and investigate the stability of sextic Lie *-derivations associated with the given functional equation via fixed point method. Also, we present a counterexample for a single case.

scholarly journals Ulam-Hyers Stability and Ulam-Hyers-Rassias Stability for Fuzzy Integrodifferential Equation

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Nguyen Ngoc Phung ◽  
Bao Quoc Ta ◽  
Ho Vu
Keyword(s):  
Fixed Point ◽  
Successive Approximation ◽  
Integrodifferential Equation ◽  
Approximation Method ◽  
Fixed Point Method ◽  
Integrodifferential Equations ◽  
Point Method ◽  
Successive Approximation Method ◽  
Rassias Stability

In this paper, we establish the Ulam-Hyers stability and Ulam-Hyers-Rassias stability for fuzzy integrodifferential equations by using the fixed point method and the successive approximation method.

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