Existence-uniqueness and fixed-point iterative method for general nonlinear fourth-order boundary value problems

2021 ◽  
Author(s):  
Shih-Hsiang Chang
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Boundary Value ◽  
Fixed Point Iterative Method

scholarly journals Existence and Iterative Method for Some Riemann Fractional Nonlinear Boundary Value Problems

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 961 ◽  
Author(s):  
Imed Bachar ◽  
Habib Mâagli ◽  
Hassan Eltayeb
Keyword(s):  
Iterative Method ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Existence And Uniqueness ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Uniqueness Of Solution ◽  
Nonlinear Boundary Value Problems ◽  
Nonlinear Boundary Value ◽  
Appl Math

In this paper, we prove the existence and uniqueness of solution for some Riemann–Liouville fractional nonlinear boundary value problems. The positivity of the solution and the monotony of iterations are also considered. Some examples are presented to illustrate the main results. Our results generalize those obtained by Wei et al (Existence and iterative method for some fourth order nonlinear boundary value problems. Appl. Math. Lett. 2019, 87, 101–107.) to the fractional setting.

scholarly journals New Contractive Mappings and Their Fixed Points in Branciari Metric Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Hayel N. Saleh ◽  
Mohammad Imdad ◽  
Thabet Abdeljawad ◽  
Mohammad Arif
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Boundary Value ◽  
Contractive Mappings

In this paper, we introduce the notion of generalized L-contractions which enlarge the class of ℒ-contractions initiated by Cho in 2018. Thereafter, we also, define the notion of L∗-contractions. Utilizing our newly introduced notions, we establish some new fixed-point theorems in the setting of complete Branciari’s metric spaces, without using the Hausdorff assumption. Moreover, some examples and applications to boundary value problems of the fourth-order differential equations are given to exhibit the utility of the obtained results.

scholarly journals Generalized Iteration Method via Green's Function for the Solution of the Fourth-order Boundary Value Problems

2021 ◽  
Vol 14 (3) ◽  
pp. 969-979
Author(s):  
Fatma Aydın Akgün ◽  
Zaur Rasulov
Keyword(s):  
Fixed Point ◽  
Green’S Function ◽  
Boundary Value Problems ◽  
Green's Function ◽  
Fourth Order ◽  
Iteration Method ◽  
Boundary Value ◽  
Fixed Point Iteration ◽  
Linear And Nonlinear ◽  
Generalized Iteration

The aim of this paper is to extend and generalize Picard-Green’s fixed point iteration method for the solution of fourth-order Boundary Value Problems. Several numerical applications to linear and nonlinear fourth-order Boundary Value Problems are discussed to illustrate the main results.

scholarly journals Approximation of the Fixed Point of Multivalued Quasi-Nonexpansive Mappings via a Faster Iterative Process with Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Godwin Amechi Okeke ◽  
Mujahid Abbas ◽  
Manuel de la Sen
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Fixed Points ◽  
Boundary Value Problems ◽  
Rate Of Convergence ◽  
Iterative Process ◽  
Numerical Experiments ◽  
Nonexpansive Mappings ◽  
Point Boundary ◽  
Fixed Point Iterative Method

In this paper, we approximate the fixed points of multivalued quasi-nonexpansive mappings via a faster iterative process and propose a faster fixed-point iterative method for finding the solution of two-point boundary value problems. We prove analytically and with series of numerical experiments that the Picard–Ishikawa hybrid iterative process has the same rate of convergence as the CR iterative process.

scholarly journals Positive Solutions of a Singular Positone and Semipositone Boundary Value Problems for Fourth-Order Difference Equations

2010 ◽  
Vol 2010 ◽  
pp. 1-16 ◽  
Author(s):  
Chengjun Yuan
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fourth Order ◽  
Difference Equations ◽  
Fixed Point Theorems ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Order Difference ◽  
Existence Of Positive Solutions

This paper studies the boundary value problems for the fourth-order nonlinear singular difference equationsΔ4u(i−2)=λα(i)f(i,u(i)),i∈[2,T+2],u(0)=u(1)=0,u(T+3)=u(T+4)=0. We show the existence of positive solutions for positone and semipositone type. The nonlinear term may be singular. Two examples are also given to illustrate the main results. The arguments are based upon fixed point theorems in a cone.

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