Abstract
In this paper, we establish some results for a Volterra–Hammerstein integral equation with modified arguments: existence and uniqueness, integral inequalities, monotony and Ulam-Hyers-Rassias stability. We emphasize that many problems from the domain of symmetry are modeled by differential and integral equations and those are approached in the stability point of view. In the literature, Fredholm, Volterra and Hammerstein integrals equations with symmetric kernels are studied. Our results can be applied as particular cases to these equations.
Highlights
Many problems from the domain of symmetry are modeled by integral equations.In this paper, we study a functional integral equation, a generalization of the equations considered in the papers [1,2,3,4].Other functional integral equations were studied in [5,6,7,8,9]
We study a functional integral equation, a generalization of the equations considered in the papers [1,2,3,4]
The main objectives of the paper are the study of some properties of the solutions of the Equation (1), among which we mention the existence and uniqueness, integral inequalities, monotony and Ulam stability
Summary
Many problems from the domain of symmetry are modeled by integral equations. In this paper, we study a functional integral equation, a generalization of the equations considered in the papers [1,2,3,4]. The equation is studied using Picard operators technique and Gronwall-type inequalities technique. Let A : X −→ X be an operator and FA = { x ∈ X | A( x ) = x } be the fixed points set of A. Let( X, →, ≤) be an ordered L−space and A, B, C : X → X three operators such that:. The main objectives of the paper are the study of some properties of the solutions of the Equation (1), among which we mention the existence and uniqueness, integral inequalities, monotony and Ulam stability. Equations of this type have multiple applications in mathematics, physics, technology, economics, etc. In papers [16,17,18] are studied integro-differential models with applications in economics, and in papers [1,5,12] are studied mathematical problems formulated on these equations
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