On Approximate Solutions of Linear and Nonlinear Singular Integral Equations

Nizami Mustafa () and Veysel Nezir ()
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Nizami Mustafa: Kafkas University, Department of Mathematics, Faculty of Science and Letters
Veysel Nezir: Kafkas University, Department of Mathematics, Faculty of Science and Letters

Chapter Chapter 19 in Current Trends in Mathematical Analysis and Its Interdisciplinary Applications, 2019, pp 737-808 from Springer

Abstract: Abstract Singular integral equation theory has broad applications to theoretical and practical investigations in mathematics, mathematical physics, hydrodynamic and elasticity theory. This fact motivated many researchers to work on this field and their studies have showed that finding approximate solutions of linear and nonlinear singular integral equations in Banach spaces provides many applications even if their definite solutions cannot be found or if there are difficulties in finding them. Thus, the central theme of the recent studies is to develop effective approximate solution methods for the linear and nonlinear singular integral equations in Banach spaces. This chapter has been devoted to investigating approximate solutions of linear and nonlinear singular integral equations in Banach spaces using technical methods such as collocation method, quadrature method, Newton–Kantorovich method, monotonic operators method, and fixed point theory depending on the type of the equations. We provide sufficient conditions for the convergence of these methods and investigate some properties.

Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-15242-0_19

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DOI: 10.1007/978-3-030-15242-0_19

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