Application of Fixed Point Results on Rational F-Contraction Mappings to Solve Boundary Value Problems

Rao, G. Venkata; Padhan, Saroj Kumar; Postolache, Mihai

doi:10.3390/sym11010070

Cited by 3 publications

(2 citation statements)

References 15 publications

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“…We denote by ∆ , the set of all mappings F : R + → R satisfying (F 1 )-(F 3 ) and continuous from the right. For more details in the direction of F-contractions, we refer the readers to [5][6][7][8][9][10].…”

Section: Definition 3 ([4]mentioning

confidence: 99%

Generalized Fixed-Point Results for Almost (α,Fσ)-Contractions with Applications to Fredholm Integral Inclusions

Al-Mezel

Ahmad

2019

Symmetry

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The purpose of this article is to define almost ( α , F σ ) -contractions and establish some generalized fixed-point results for a new class of contractive conditions in the setting of complete metric spaces. In application, we apply our fixed-point theorem to prove the existence theorem for Fredholm integral inclusions ϖ ( t ) ∈ f ( t ) + ∫ 0 1 K ( t , s , x ( s ) ) ϑ s , t ∈ [ 0 , 1 ] where f ∈ C [ 0 , 1 ] is a given real-valued function and K : [ 0 , 1 ] × [ 0 , 1 ] × R → K c v ( R ) is a given multivalued operator, where K c v represents the family of nonempty compact and convex subsets of R and ϖ ∈ C [ 0 , 1 ] is the unknown function. We also provide a non-trivial example to show the significance of our main result.

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Section: Definition 3 ([4]mentioning

confidence: 99%

Generalized Fixed-Point Results for Almost (α,Fσ)-Contractions with Applications to Fredholm Integral Inclusions

Al-Mezel

Ahmad

2019

Symmetry

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“…Truhlar et al have proposed the boundary value method (BVM), Dahlquist et al have studied the two-step boundary method, and Noor et al have investigated the convergence and stability of the three and four step boundary value method. The results have shown BVM can control global error and has a high accuracy and great advantages in stability [17][18][19][20][21][22]. However, BVM still has some disadvantages such as its heavy and deficient calculation and it cannot change the step size.…”

Section: Introductionmentioning

confidence: 99%

Fast Calculation Method for Transient Response of Transmission Line Based on Chebyshev Pseudospectral–Two-Step Three-Order Boundary Value Coupled Method

Yuan

et al. 2019

Symmetry

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A Chebyshev pseudospectral–two-step three-order boundary value coupled method is proposed and presented for handling the issue associated with complicated calculation, low precision, and poor stability in the process of transient response of transmission line. The first order differential equation in time domain is obtained via dispersing the telegraph equation in space domain by utilizing the pseudospectral method (PSM) based on Chebyshev polynomial. Then the two-step three-order boundary value method (BVM3) is presented and employed to resolve the obtained differential equation, so the numerical solution of the space discrete points can be obtained. Furthermore, the Chebyshev pseudospectral–two-step three-order boundary value coupled method (PSM-BVM3) is presented and compared with the Chebyshev pseudospectral–two-step two order boundary value coupled method (PSM-BVM2), the pseudospectral–differential quadrature method (PSM-DQM), and the pseudospectral method–trapezoid rule (PSM-TR) to validate the feasibility of the new proposed method. Theoretical analysis and numerical simulation reveal that the proposed Chebyshev PSM-BVM3 has a higher performance than the conventional method. For the proposed Chebyshev PSM-BVM3, the higher precision, efficiency, and numerical stability can be obtained and achieved only with fewer discrete points in the space domain, which is suitable for solving the transient response of transmission line. The proposed PSM-BVM3 can improve the drawback of numerical instability of the PSM and can also improve the disadvantage of the BVM as it is not easy to change the latter’s timestep size.

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A survey: F-contractions with related fixed point results

Karapınar

Fulga

Agarwal

2020

J. Fixed Point Theory Appl.

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Application of Fixed Point Results on Rational F-Contraction Mappings to Solve Boundary Value Problems

Cited by 3 publications

References 15 publications

Generalized Fixed-Point Results for Almost (α,Fσ)-Contractions with Applications to Fredholm Integral Inclusions

Generalized Fixed-Point Results for Almost (α,Fσ)-Contractions with Applications to Fredholm Integral Inclusions

Fast Calculation Method for Transient Response of Transmission Line Based on Chebyshev Pseudospectral–Two-Step Three-Order Boundary Value Coupled Method

A survey: F-contractions with related fixed point results

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