scholarly journals Integral Equations for Exterior Scattering That Have a Unique Solution at All Frequencies

1969 ◽  
Vol 46 (1A) ◽  
pp. 117-117
Author(s):  
K. M. Mitzner
Keyword(s):  
Unique Solution ◽  
Integral Equations

scholarly journals Solution of system of the Fredholm integral equation of the first kind

2021 ◽  
Vol 1 (4) ◽  
pp. 1-7
Author(s):  
Vladimir Uskov
Keyword(s):  
Integral Equation ◽  
Unique Solution ◽  
Integral Equations ◽  
Fredholm Integral Equation ◽  
Production Costs ◽  
Fredholm Integral Equations ◽  
System Of Equations ◽  
Blurred Image ◽  
Basic Functions ◽  
Image Production

The article is devoted to the study of a system of two inhomogeneous Fredholm integral equations of the first kind with two required functions depending on one variable. Integral equations describe the restoration of a blurred image, production costs, etc. Fredholm integral equations with one desired function have been considered in many works, but relatively few works have been devoted to systems of such equations. The questions of stability for the solution of systems and the construction of a regularizing system of equations were investigated, but the solution was not constructed in an explicit form. In this paper, the kernels depend on two variables. The case is considered: in the kernels and inhomogeneities, the variables are separated in the equations; these functions are decomposed on the basis of two functions on the interval of integration. Examples of basic functions are given. A condition is determined under which the system has a unique solution in the chosen basis, formulated as a theorem. The solution is found in the form of an expansion in this basis. To illustrate the results obtained, an example is considered

scholarly journals FIXED POINT RESULTS IN COMPLEX VALUED METRIC SPACES WITH AN APPLICATION

2021 ◽  
pp. 237
Author(s):  
Rashwan A. Rashwan ◽  
Hasanen A. Hammad ◽  
Liliana Guran
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Unique Solution ◽  
Integral Equations ◽  
Point Theorem ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Urysohn Integral Equations ◽  
Complex Valued

In this paper, we introduce fixed point theorem for a general contractive condition in complex valued metric spaces. Also, some important corollaries under this contractive condition areobtained. As an application, we find a unique solution for Urysohn integral equations and some illustrative examples are given to support our obtaining results. Our results extend and generalize the results of Azam et al. [2] and some other known results in the literature.

scholarly journals The Solutions of Mixed Monotone Fredholm-Type Integral Equations in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Hua Su
Keyword(s):  
Boundary Value Problem ◽  
Banach Spaces ◽  
Unique Solution ◽  
Integral Equations ◽  
Nonlinear Ordinary Differential Equations ◽  
Point Boundary ◽  
Fredholm Type ◽  
Monotone Iterative ◽  
Type Integral ◽  
Ordered Banach Spaces

By introducing new definitions ofϕconvex and-φconcave quasioperator andv0quasilower andu0quasiupper, by means of the monotone iterative techniques without any compactness conditions, we obtain the iterative unique solution of nonlinear mixed monotone Fredholm-type integral equations in Banach spaces. Our results are even new toϕconvex and-φconcave quasi operator, and then we apply these results to the two-point boundary value problem of second-order nonlinear ordinary differential equations in the ordered Banach spaces.

On multivalued stochastic integral equations driven by semimartingales

2019 ◽  
Vol 26 (3) ◽  
pp. 423-436
Author(s):  
Marek T. Malinowski
Keyword(s):  
Unique Solution ◽  
Integral Equations ◽  
Stochastic Integral ◽  
Successive Approximations ◽  
Stochastic Integral Equations

Abstract We consider multivalued stochastic integral equations driven by semimartingales. Such equations are formulated in two different forms, i.e., using multivalued stochastic up-trajectory and trajectory integrals, which are not equivalent. By the successive approximations method, we show the existence of a unique solution to each equation under a condition much weaker than the Lipschitz one. We indicate that the solutions are stable under small changes of the equation data. The results have immediate implications for solutions to single-valued stochastic integral equations driven by semimartingales.

scholarly journals Analytical Solution of Urysohn Integral Equations by Fixed Point Technique in Complex Valued Metric Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 852 ◽  
Author(s):  
Hasanen A. Hammad ◽  
Manuel De la Sen
Keyword(s):  
Fixed Point ◽  
Analytical Solution ◽  
Unique Solution ◽  
Integral Equations ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Fixed Point Result ◽  
Urysohn Integral Equations ◽  
Fixed Point Technique ◽  
Complex Valued

The purpose of this article is to introduce a fixed point result for a general contractive condition in the context of complex valued metric spaces. Also, some important corollaries under this contractive condition are obtained. As an application, we find a unique solution for Urysohn integral equations, and some illustrative examples are given to support our obtaining results. Our results extend and generalize the results of Azam et al. Previous known related results in the literarure and some other known results in the literature.

scholarly journals Quadratically converging iterative schemes for nonlinear Volterra integral equations and an application

1997 ◽  
Vol 10 (2) ◽  
pp. 169-178 ◽  
Author(s):  
Sudhakar G. Pandit
Keyword(s):  
Boundary Layer ◽  
Unique Solution ◽  
Integral Equations ◽  
Boundary Layer Theory ◽  
Volterra Integral Equations ◽  
Theory Problem ◽  
Iterative Schemes

A generalized quasilinear technique is employed to derive iterative schemes for nonlinear Volterra integral equations under various monotonicity and convexity (concavity) conditions on the kernels. The iterates in the schemes are linear, and converge monotonically, uniformly and quadratically to the unique solution. An application to a boundary-layer theory problem and examples illustrating the results are presented.

scholarly journals Fixed point results for a pair of fuzzy mappings and related applications in b-metric like spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Tahair Rasham ◽  
Giuseppe Marino ◽  
Aqeel Shahzad ◽  
Choonkill Park ◽  
Abdullah Shoaib
Keyword(s):  
Functional Equation ◽  
Dynamic Programming ◽  
Fixed Point ◽  
Unique Solution ◽  
Integral Equations ◽  
Bounded Solution ◽  
System Of Integral Equations

AbstractThis paper is devoted to finding out some realization of the concept of b-metric like space. First, we attain a fixed point for two fuzzy mappings satisfying a suitable requirement of contractiveness. Subsequently, we apply such a result to graphic contractions. Also, we attain a unique solution for a system of integral equations, and lastly we give an application to ensure that there exists a common bounded solution of a suitable functional equation in dynamic programming.

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