scholarly journals A Fixed Point Technique for Set-Valued Contractions with Supportive Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Hasanen A. Hammad ◽  
Manuel De la Sen
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Harmonic Oscillator ◽  
Fredholm Integral Equation ◽  
Multivalued Mappings ◽  
Initial Value ◽  
Infinite Systems ◽  
Damped Harmonic Oscillator ◽  
Fixed Point Technique ◽  
Theoretical Results

In this manuscript, exciting fixed point results for a pair of multivalued mappings justifying rational Gupta-Saxena type Ω -contractions in the setting of extended b -metric-like spaces are established. The theoretical results have also been strengthened by some nontrivial examples. Finally, the theoretical results are used to study the existence of the solution of Fredholm integral equation which arises from the damped harmonic oscillator, to study initial value problem which arises from Newton’s law of cooling and to study infinite systems of fractional ordinary differential equations (ODEs).

scholarly journals A Solution of Fredholm Integral Equation by Using the Cyclic η s q -Rational Contractive Mappings Technique in b-Metric-Like Spaces

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1184 ◽  
Author(s):  
Hasanen A. Hammad ◽  
Manuel De la Sen
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Directed Graph ◽  
Fredholm Integral Equation ◽  
Fixed Point Theorems ◽  
Contractive Mappings ◽  
Theoretical Results

In this article, the notion of cyclic η s q -rational contractive mappings is discussed and some fixed point theorems in the context of complete b-metric-like spaces are showed. Here, the obtained consequences unify, extend and generalize various comparable known results. Furthermore, new common fixed point outcomes in a directed graph are demonstrated. Moreover, some useful examples are discussed to justify our theoretical results and finding a solution of Fredholm integral equation was discussed as enforcement.

scholarly journals Numerical Treatment of Fixed Point Applied to the Nonlinear Fredholm Integral Equation

2009 ◽  
Vol 2009 (1) ◽  
pp. 735638 ◽  
Author(s):  
MI Berenguer ◽  
MV Fernández Muñoz ◽  
AI Garralda Guillem ◽  
M Ruiz Galán
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fredholm Integral Equation ◽  
Numerical Treatment ◽  
Nonlinear Fredholm Integral Equation

scholarly journals Multivalued generalizations of fixed point results in fuzzy metric spaces

2016 ◽  
Vol 21 (2) ◽  
pp. 211-22 ◽  
Author(s):  
Tatjana Došenovic ◽  
Dušan Rakic ◽  
Biljana Caric ◽  
Stojan Radenovic
Keyword(s):  
Fixed Point ◽  
Distance Function ◽  
Metric Space ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Multivalued Mappings ◽  
Altering Distance Function ◽  
Fuzzy Metric ◽  
Altering Distance ◽  
Theoretical Results

This paper attempts to prove fixed and coincidence point results in fuzzy metric space using multivalued mappings. Altering distance function and multivalued strong {bn}-fuzzy contraction are used in order to do that. Presented theorems are generalization of some well known single valued results. Two examples are given to support the theoretical results.

scholarly journals A Triangle Algorithm of Padé-Type Approximant for Two-Dimensional Fredholm Integral Equations of the Second Kind

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Meilan Sun ◽  
Chuanqing Gu
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Fredholm Integral Equation ◽  
Recursive Algorithm ◽  
High Order ◽  
Fredholm Integral Equations ◽  
Two Dimensional ◽  
Initial Value ◽  
Numerical Examples ◽  
Type Approximation

The function-valued Padé-type approximation (2DFPTA) is used to solve two-dimensional Fredholm integral equation of the second kind. In order to compute 2DFPTA, a triangle recursive algorithm based on Sylvester identity is proposed. The advantage of this algorithm is that, in the process of calculating 2DFPTA to avoid the calculation of the determinant, it can start from the initial value, from low to high order, and gradually proceeds. Compared with the original two methods, the numerical examples show that the algorithm is effective.

On the stability for the fuzzy initial value problem

2020 ◽  
Vol 39 (5) ◽  
pp. 7747-7755
Author(s):  
Ngo Van Hoa ◽  
Tofigh Allahviranloo ◽  
Ho Vu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Initial Value Problem ◽  
Ulam Stability ◽  
Initial Value ◽  
The Stability ◽  
Theoretical Results ◽  
Rassias Stability

In this paper, we present the Hyers–Ulam stability and Hyers–Ulam-Rassias stability (HU-stability and HUR-stability for short) for fuzzy initial value problem (FIVP) by using fixed point theorem. We improve and extend some known results on the stability for FDEs by dropping some assumptions. Some examples illustrate the theoretical results.

scholarly journals Existence of Mild Solutions for the Elastic Systems with Structural Damping in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Hongxia Fan ◽  
Yongxiang Li ◽  
Pengyu Chen
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Elastic System ◽  
Mild Solutions ◽  
Structural Damping ◽  
Initial Value ◽  
Operator Semigroups ◽  
Elastic Systems ◽  
Theoretical Results

This paper deals with the existence and uniqueness of mild solutions for a second order evolution equation initial value problem in a Banach space, which can model an elastic system with structural damping. The discussion is based on the operator semigroups theory and fixed point theorem. In addition, an example is presented to illustrate our theoretical results.

scholarly journals GENERAL SOLUTION OF THE QUANTUM DAMPED HARMONIC OSCILLATOR II: SOME EXAMPLES

2009 ◽  
Vol 06 (02) ◽  
pp. 225-231 ◽  
Author(s):  
KAZUYUKI FUJII ◽  
TATSUO SUZUKI
Keyword(s):  
General Solution ◽  
Coherent State ◽  
Harmonic Oscillator ◽  
Infinite Series ◽  
Operator Algebra ◽  
Preceding Paper ◽  
Initial Value ◽  
Damped Harmonic Oscillator ◽  
Density Operators ◽  
Algebra Level

In the preceding paper (arXiv: 0710.2724 [quant-ph]) we have constructed the general solution for the master equation of quantum damped harmonic oscillator, which is given by the complicated infinite series in the operator algebra level. In this paper we give the explicit and compact forms to solutions (density operators) for some initial values. In particular, the compact one for the initial value based on a coherent state is given, which has not been given as far as we know. Moreover, some related problems are presented.

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