Tikhonov regularization is a popular and effective method for the approximate solution of illposed problems, including Fredholm equations of the first kind. The Tikhonov method works well when the solution of the equation is well-behaved, but fails for solutions with irregularities, such as jump discontinuities. In this paper we develop a method that overcomes the limitations of the standard Ti...

At the 2012 Republican National Convention in Tampa, in an interview with NPR’s Robert Siegel, former Congressman Thomas Davis (R-Va) talked about the future of American politics. “What you’re finding is that both parties are just moving right and left,” he said. Siegel then asked if Davis thought this would change. CongressmanDavis replied that he thought it would get worse. “And I’ll explain ...

in this paper, we improve some recent coupled fixed point resultsfor single-valued operators in the framework of ordered $b$-metricspaces established by bota et al. [m-f. bota, a. petrusel, g.petrusel and b. samet, coupled fixed point theorems forsingle-valued operators in b-metric spaces, fixed point theoryappl. (2015) 2015:231]. also, we prove that perov-type fixed pointtheorem in ordered gen...

In this paper, we are dealing with the ill-posed Cauchy problem for an elliptic operator. To do this, interpret as inverse problem, and therefore a controllability problem. This point of view induces regularization method that makes it possible, on one hand, to characterize existence regular solution On other possible obtain singular optimality system optimal control, without resorting any addi...