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.

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 Controlled b-Branciari metric type spaces and related fixed point theorems with applications

Filomat ◽  
2020 ◽  
Vol 34 (13) ◽  
pp. 4253-4269
Author(s):  
Sumaiya Zubair ◽  
Kalpana Gopalan ◽  
Thabet Abdeljawad
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Existence Of Solution ◽  
Fixed Point Method ◽  
Fredholm Integral Equations ◽  
Effective Solution ◽  
Type Space ◽  
Type Spaces

In this manuscript, we present and develop different F-contraction methods using new kinds of contractions, namely F1-contraction and extended F1-contraction in the context of controlled b-Branciari metric type space. We then suggest an easy and effective solution for Fredholm integral equations using the fixed point method in the framework of controlled b-Branciari metric type space. We also provide an illustrative example for the existence of solution to second order boundary value problem to demonstrate the efficiency of the work that has been developed.

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.

scholarly journals Homomorphisms and derivations in C∗-ternary algebras via fixed point method

2012 ◽  
Vol 2012 (1) ◽  
pp. 137 ◽  
Author(s):  
HM Kenari ◽  
Reza Saadati ◽  
Choonkil Park
Keyword(s):  
Fixed Point ◽  
Fixed Point Method ◽  
Point Method ◽  
Ternary Algebras
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