Solvability of a Volterra–Stieltjes integral equation in the class of functions having limits at infinity

Banaś, Józef; Dubiel, Agnieszka

doi:10.14232/ejqtde.2017.1.53

Cited by 7 publications

(3 citation statements)

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“…Many researchers have investigated the solvability and asymptotic stability for different types of integral equations or systems of integral equations in various classes of functions, for example, [30][31][32]. The main technique used in these papers is Darbo's fixed point theorem via the Concept of Measure of Noncompactness [17][18][19][20][21][22][33][34][35].…”

Section: Discussionmentioning

confidence: 99%

New Aspects on the Solvability of a Multidimensional Functional Integral Equation with Multivalued Feedback Control

Elsayed

Hashem

Al-Issa

2023

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The current study demonstrates the existence of solutions to a multidimensional functional integral equation with multivalued feedback. We seek solutions for the multidimensional functional problem that is defined, continuous, and bounded on the semi-infinite interval. Our proof is based on the technique associated with measures of noncompactness by a given modulus of continuity in the space in BC(R+). Also, some sufficient conditions are investigated to demonstrate the asymptotic stability of the solutions to that multidimensional functional equation. Additionally, we give an example and some particular cases to illustrate our outcomes.

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Section: Discussionmentioning

confidence: 99%

New Aspects on the Solvability of a Multidimensional Functional Integral Equation with Multivalued Feedback Control

Elsayed

Hashem

Al-Issa

2023

Axioms

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“…Banaś in [16][17][18][19][20][21][22] successfully used the method connected to a measure of noncompactness in the Banach space BC(R + ) (which consists of all bounded and continuous functions on R + ) to determine the existence of asymptotically stable solutions to some integral and quadratic integral equations (see [18,19]). Furthermore, for the solvability of some problems in the half-line axis, see [23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Investigating Asymptotic Stability for Hybrid Cubic Integral Inclusion with Fractal Feedback Control on the Real Half-Axis

2023

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In this paper, we discuss the existence of solutions for a hybrid cubic delayed integral inclusion with fractal feedback control. We are seeking solutions for these hybrid cubic delayed integral inclusions that are defined, continuous, and bounded on the semi-infinite interval. Our proof is based on the technique associated with measures of noncompactness by a given modulus of continuity in the space in BC(R+). In addition, some sufficient conditions are investigated to demonstrate the asymptotic stability of the solutions of that integral inclusion. Finally, some cases analyzed are in the presence and absence of the control variable, and two examples are provided in order to indicate the validity of the assumptions.

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“…Among the many integral equations that were established in mathematical analysis and were stratified to many areas of engineering and real life sciences, an efficient and effective role is played by integral equations of fractional kernels [8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Existence results for nonlinear coupled system of integral equations of Urysohn Volterra-Chandrasekhar mixed type

Nabil

2020

Demonstratio Mathematica

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The combined systems of integral equations have become of great importance in various fields of sciences such as electromagnetic and nuclear physics. New classes of the merged type of Urysohn Volterra-Chandrasekhar quadratic integral equations are proposed in this paper. This proposed system involves fractional Urysohn Volterra kernels and also Chandrasekhar kernels. The solvability of a coupled system of integral equations of Urysohn Volterra-Chandrasekhar mixed type is studied. To realize the existence of a solution of those mixed systems, we use the Perov’s fixed point combined with the Leray-Schauder fixed point approach in generalized Banach algebra spaces.

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Solvability of a Volterra–Stieltjes integral equation in the class of functions having limits at infinity

Cited by 7 publications

References 0 publications

New Aspects on the Solvability of a Multidimensional Functional Integral Equation with Multivalued Feedback Control

New Aspects on the Solvability of a Multidimensional Functional Integral Equation with Multivalued Feedback Control

Investigating Asymptotic Stability for Hybrid Cubic Integral Inclusion with Fractal Feedback Control on the Real Half-Axis

Existence results for nonlinear coupled system of integral equations of Urysohn Volterra-Chandrasekhar mixed type

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