scholarly journals Solvability of infinite systems of nonlinear integral equations in two variables by using semi-analytic method

Filomat ◽  
2019 ◽  
Vol 33 (16) ◽  
pp. 5375-5386
Author(s):  
Anupam Das ◽  
Bipan Hazarika ◽  
H.M. Srivastava ◽  
Mohsen Rabbani ◽  
R. Arab
Keyword(s):  
Integral Equations ◽  
Sequence Space ◽  
Existence Of Solution ◽  
Iteration Algorithm ◽  
Analytic Method ◽  
Nonlinear Integral Equations ◽  
Validity Of Results ◽  
Infinite Systems ◽  
Banach Sequence Space ◽  
Banach Sequence

In this article, we generalize and investigate existence of solution for infinite systems of nonlinear integral equations with two variables in a given Banach sequence space BC(R+ x R+,c) using Meir-Keeler condensing and noncompactness. Validity of results are shown with the help of an illustrative example. We also introduce a coupled semi-analytic method in the case of two variables in order to construct an iteration algorithm to find a numerical solution for above-mentioned problem. The numerical results show that the produced sequence for approximating the solution in the examples is in the Banach sequence space BC(R+ x R+,c) itself.

Upper lp-estimates in vector sequence spaces, with some applications

1993 ◽  
Vol 113 (2) ◽  
pp. 329-334 ◽  
Author(s):  
Jesús M. F. Castillo ◽  
Fernando Sánchez
Keyword(s):  
Banach Spaces ◽  
Sequence Space ◽  
Sequence Spaces ◽  
Vector Sequence ◽  
Lp Estimates ◽  
Banach Sequence Space ◽  
Banach Sequence

In [11], Partington proved that if λ is a Banach sequence space with a monotone basis having the Banach-Saks property, and (Xn) is a sequence of Banach spaces each having the Banach-Saks property, then the vector sequence space ΣλXn has this same property. In addition, Partington gave an example showing that if λ and each Xn, have the weak Banach-Saks property, then ΣλXn need not have the weak Banach-Saks property.

scholarly journals Hermitian operators and isometries on sums of Banach spaces

1989 ◽  
Vol 32 (2) ◽  
pp. 169-191 ◽  
Author(s):  
R. J. Fleming ◽  
J. E. Jamison
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Sequence Space ◽  
Reflexive Banach Space ◽  
Geometric Theory ◽  
Orlicz Sequence Space ◽  
Vector Sequence ◽  
Banach Sequence Space ◽  
Banach Sequence

Let E be a Banach sequence space with the property that if (αi) ∈ E and |βi|≦|αi| for all i then (βi) ∈ E and ‖(βi)‖E≦‖(αi)‖E. For example E could be co, lp or some Orlicz sequence space. If (Xn) is a sequence of real or complex Banach spaces, then E can be used to construct a vector sequence space which we will call the E sum of the Xn's and symbolize by ⊕EXn. Specifically, ⊕EXn = {(xn)|(xn)∈Xn and (‖xn‖)∈E}. The E sum is a Banach space with norm defined by: ‖(xn)‖ = ‖(‖xn‖)‖E. This type of space has long been the source of examples and counter-examples in the geometric theory of Banach spaces. For instance, Day [7] used E=lp and Xk=lqk, with appropriate choice of qk, to give an example of a reflexive Banach space not isomorphic to any uniformly conves Banach space. Recently VanDulst and Devalk [33] have considered Orlicz sums of Banach spaces in their studies of Kadec-Klee property.

scholarly journals Nonwandering operators in Banach space

2005 ◽  
Vol 2005 (24) ◽  
pp. 3895-3908 ◽  
Author(s):  
Lixin Tian ◽  
Jiangbo Zhou ◽  
Xun Liu ◽  
Guangsheng Zhong
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Sequence Space ◽  
Separable Banach Space ◽  
Infinite Dimensional ◽  
Banach Sequence Space ◽  
Background Space ◽  
Physical Background ◽  
Structurally Stable ◽  
Banach Sequence

We introduce nonwandering operators in infinite-dimensional separable Banach space. They are new linear chaotic operators and are relative to hypercylic operators, but different from them. Firstly, we show some examples for nonwandering operators in some typical infinite-dimensional Banach spaces, including Banach sequence space and physical background space. Then we present some properties of nonwandering operators and the spectra decomposition of invertible nonwandering operators. Finally, we obtain that invertible nonwandering operators are locally structurally stable.

scholarly journals Iterative Method for a System of Nonlinear Fredholm Integral Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Keyan Wang ◽  
Qisheng Wang
Keyword(s):  
Integral Equations ◽  
Rates Of Convergence ◽  
Fredholm Integral Equations ◽  
Iteration Algorithm ◽  
Nonlinear Integral Equations ◽  
Approximation Solution ◽  
Fredholm Type ◽  
Integration Rule ◽  
Nonlinear Fredholm Integral Equations ◽  
The Fixed Point Theorem

In this paper, the iteration method is proposed to solve a class of system of Fredholm-type nonlinear integral equations. First, the existence and uniqueness of solution are theoretically proven by the fixed-point theorem. Second, the approximation solution method is given by using the appropriate integration rule. The error analysis for the approximated solution with the exact solution is discussed for infinity-norm, and the rates of convergence are obtained. Furthermore, an iteration algorithm is constructed, and the convergence of the proposed numerical method is rigorously derived. Finally, some numerical examples are given to illustrate the theoretical results.

Application of Measure of Noncompactness to Infinite Systems of Differential Equations

2013 ◽  
Vol 56 (2) ◽  
pp. 388-394 ◽  
Author(s):  
M. Mursaleen
Keyword(s):  
Differential Equations ◽  
Sequence Space ◽  
Measure Of Noncompactness ◽  
Existence Results ◽  
Sequence Spaces ◽  
Measures Of Noncompactness ◽  
Infinite Systems ◽  
Systems Of Differential Equations ◽  
Banach Sequence Spaces ◽  
Banach Sequence

AbstractIn this paper we determine theHausdorff measure of noncompactness on the sequence space n(ϕ) ofW. L. C. Sargent. Further we apply the technique of measures of noncompactness to the theory of infinite systems of differential equations in the Banach sequence spaces n(ϕ) and m(ϕ). Our aim is to present some existence results for infinite systems of differential equations formulated with the help of measures of noncompactness.

scholarly journals Fixed Point Results for a Class of Monotone Nonexpansive Type Mappings in Hyperbolic Spaces

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Rameshwar Pandey ◽  
Rajendra Pant ◽  
Ahmed Al-Rawashdeh
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Existence Results ◽  
Hyperbolic Spaces ◽  
Iteration Algorithm ◽  
Nonlinear Integral Equations ◽  
Convergence Results ◽  
Partially Hyperbolic

We consider a wider class of nonexpansive type mappings and present some fixed point results for this class of mapping in partially hyperbolic spaces. Indeed, first we obtain some existence results for this class of mappings. Next, we present some convergence results for an iteration algorithm for the same class of mappings. Some illustrative nontrivial examples have also been discussed. Finally, we provide an application of our results to nonlinear integral equations.

scholarly journals Geraghty type contractions in fuzzy b-metric spaces with application to integral equations

Filomat ◽  
2020 ◽  
Vol 34 (9) ◽  
pp. 3083-3098
Author(s):  
Muhammad Ashraf ◽  
Rashid Ali ◽  
Nawab Hussain
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Metric Spaces ◽  
Existence Of Solution ◽  
Nonlinear Integral Equations ◽  
Type Contraction

In this paper, we study the notion of a fuzzy b-metric space and establish certain fixed point results for Geraghty-type contraction in the setting of G-complete fuzzy b-metric space. We furnish an example to illustrate our main result. Our results extend and generalize the existing results in the literature. An application related to our main result for the existence of solution of nonlinear integral equations is also presented.

scholarly journals On a class of infinite system of third-order differential equations in lp via measure of noncompactness

Filomat ◽  
2020 ◽  
Vol 34 (11) ◽  
pp. 3861-3870
Author(s):  
E. Pourhadi ◽  
M. Mursaleen ◽  
R. Saadati
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Sequence Space ◽  
Measure Of Noncompactness ◽  
Infinite System ◽  
Third Order ◽  
Banach Sequence Space ◽  
Existence Of Periodic Solutions ◽  
Banach Sequence

In this paper, with the help of measure of noncompactness together with Darbo-type fixed point theorem, we focus on the infinite system of third-order differential equations u???i + au??i + bu?i + cui = fi(t, u1(t), u2(t),...) where fi ? C(R x R?,R) is ?-periodic with respect to the first coordinate and a,b,c ? R are constants. The aim of this paper is to obtain the results with respect to the existence of ?-periodic solutions of the aforementioned system in the Banach sequence space lp (1 ? p < ?) utilizing the respective Green?s function. Furthermore, some examples are provided to support our main results.

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