Abstract
In the present work, we consider one of the possible generalizations of linear and nonlinear Volterra integral equations of the second kind in the case when the independent variable belongs to an arbitrary noncompact metric space. Sufficient conditions are obtained for the existence of solutions of Volterra-type integral equations in the nonhomogeneous case. Some applications of the obtained results to the integral inequalities are given. MSC:35Q99, 35R35, 65M12, 65M70.
Highlights
1 Introduction Integral equations and inequalities have been of considerable significance in mathematics and have held a central place in the attention of mathematicians during the last few decades
In the past few years, integral equations have proved to be of tremendous use in several applied fields, such as population dynamics, spread of epidemics, automatic control theory, network theory and the dynamics of nuclear reactors
The techniques of these proofs, in general based on the classical mathematical analysis, lead up to virtuosity and significantly depend on the number of independent variables and the geometry of the domain of integration
Summary
Integral equations and inequalities have been of considerable significance in mathematics and have held a central place in the attention of mathematicians during the last few decades. (S ) For each x ∈ and every f ∈ C(Mx, B), there exist numbers δ(Mx, f ) > and L(Mx, f , δ) > such that for every functions g ∈ C(Mx, B) for which f – g Mx < δ, the following inequality holds: sup Q s, y, f (y) – Q s, y, g(y)
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