scholarly journals Solutions of an infinite system of integral equations of Volterra-Stieltjes type in the sequence spaces $\ell_{p} (1

2020 ◽  
Vol 5 (4) ◽  
pp. 3791-3808
Author(s):  
Ayub Samadi ◽  
◽  
M. Mosaee Avini ◽  
M. Mursaleen ◽  
◽  
...  
Keyword(s):  
Integral Equations ◽  
Infinite System ◽  
Sequence Spaces ◽  
System Of Integral Equations ◽  
Stieltjes Type

scholarly journals Solvability of an infinite system of integral equations on the real half-axis

2020 ◽  
Vol 10 (1) ◽  
pp. 202-216
Author(s):  
Józef Banaś ◽  
Weronika Woś
Keyword(s):  
Integral Equations ◽  
Measure Of Noncompactness ◽  
Infinite System ◽  
Main Tool ◽  
Supremum Norm ◽  
Nonlinear Integral Equations ◽  
Measures Of Noncompactness ◽  
System Of Integral Equations ◽  
The Real ◽  
Half Axis

Abstract The aim of the paper is to investigate the solvability of an infinite system of nonlinear integral equations on the real half-axis. The considerations will be located in the space of function sequences which are bounded at every point of the half-axis. The main tool used in the investigations is the technique associated with measures of noncompactness in the space of functions defined, continuous and bounded on the real half-axis with values in the space l∞ consisting of real bounded sequences endowed with the standard supremum norm. The essential role in our considerations is played by the fact that we will use a measure of noncompactness constructed on the basis of a measure of noncompactness in the mentioned sequence space l∞. An example illustrating our result will be included.

scholarly journals Fixed-Point Results for Generalized α -Admissible Hardy-Rogers’ Contractions in Cone b 2 -Metric Spaces over Banach’s Algebras with Application

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Ziaul Islam ◽  
Muhammad Sarwar ◽  
Manuel de la Sen
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Infinite System ◽  
Metric Spaces ◽  
Existence Of A Solution ◽  
System Of Integral Equations

In the current manuscript, the notion of a cone b 2 -metric space over Banach’s algebra with parameter b ≻ ¯ e is introduced. Furthermore, using α -admissible Hardy-Rogers’ contractive conditions, we have proven fixed-point theorems for self-mappings, which generalize and strengthen many of the conclusions in existing literature. In order to verify our key result, a nontrivial example is given, and as an application, we proved a theorem that shows the existence of a solution of an infinite system of integral equations.

scholarly journals Some Coincidence and Common Fixed-Point Results on Cone b 2 -Metric Spaces over Banach Algebras with Applications to the Infinite System of Integral Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Ziaul Islam ◽  
Muhammad Sarwar ◽  
Doaa Filali ◽  
Fahd Jarad
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Infinite System ◽  
Metric Spaces ◽  
Banach Algebras ◽  
System Of Integral Equations ◽  
Different Types ◽  
Common Fixed Point Theorems

In this article, common fixed-point theorems for self-mappings under different types of generalized contractions in the context of the cone b 2 -metric space over the Banach algebra are discussed. The existence results obtained strengthen the ones mentioned previously in the literature. An example and an application to the infinite system of integral equations are also presented to validate the main results.

scholarly journals Solvability of an infinite system of nonlinear integral equations of Volterra-Hammerstein type

2019 ◽  
Vol 9 (1) ◽  
pp. 1187-1204
Author(s):  
Agnieszka Chlebowicz
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Function Space ◽  
Measure Of Noncompactness ◽  
Infinite System ◽  
Nonlinear Integral Equations ◽  
System Of Integral Equations ◽  
Half Axis ◽  
Suitable Measure

Abstract The purpose of the paper is to study the solvability of an infinite system of integral equations of Volterra-Hammerstein type on an unbounded interval. We show that such a system of integral equations has at least one solution in the space of functions defined, continuous and bounded on the real half-axis with values in the space l1 consisting of all real sequences whose series is absolutely convergent. To prove this result we construct a suitable measure of noncompactness in the mentioned function space and we use that measure together with a fixed point theorem of Darbo type.

scholarly journals One approach to the axisymmetric problem of impact of fine shells of the S.P. Timoshenko type on elastic half-space

2021 ◽  
pp. 77-89
Author(s):  
Vladislav Bogdanov
Keyword(s):  
Integral Equations ◽  
Half Space ◽  
Axisymmetric Problem ◽  
Infinite System ◽  
Elastic Half Space ◽  
Wave Processes ◽  
System Of Integral Equations ◽  
Timoshenko Type ◽  
Dynamics Problems ◽  
The Impact

Refined model of S.P. Timoshenko makes it possible to consider the shear and the inertia rotation of the transverse section of the shell. Disturbances spread in the shells of S.P. Timoshenko type with finite speed. Therefore, to study the dynamics of propagation of wave processes in the fine shells of S.P. Timoshenko type is an important aspect as well as it is important to investigate a wave processes of the impact, shock in elastic foundation in which a striker is penetrating. The method of the outcoming dynamics problems to solve an infinite system of integral equations Volterra of the second kind and the convergence of this solution are well studied. Such approach has been successfully used for cases of the investigation of problems of the impact a hard bodies and an elastic fine shells of the Kirchhoff-Love type on elastic a half-space and a layer. In this paper an attempt is made to solve the axisymmetric problem of the impact of an elastic fine spheric shell of the S.P. Timoshenko type on an elastic half-space using the method of the outcoming dynamics problems to solve an infinite system of integral equations Volterra of the second kind. It is shown that this approach is not acceptable for investigated in this paper axisymmetric problem. The discretization using the Gregory methods for numerical integration and Adams for solving the Cauchy problem of the reduced infinite system of Volterra equations of the second kind results in a poorly defined system of linear algebraic equations: as the size of reduction increases the determinant of such a system to aim at infinity. This technique does not allow to solve plane and axisymmetric problems of dynamics for fine shells of the S.P. Timoshenko type and elastic bodies. This shows the limitations of this approach and leads to the feasibility of developing other mathematical approaches and models. It should be noted that to calibrate the computational process in the elastoplastic formulation at the elastic stage, it is convenient and expedient to use the technique of the outcoming dynamics problems to solve an infinite system of integral equations Volterra of the second kind.

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