In this work, we investigate nonlinear boundary value problems for impulsive differential equations with causal operators. Our boundary condition is given by a nonlinear function, and more general than ones given before. To begin with, we prove a comparison theorem. Then by using this theorem, we show the existence of solutions for linear problems. Finally, by using the monotone iterative techn...

This paper is devoted to the study of periodic boundary value problems for nonlinear third order di¤erential equations subjected to impulsive e¤ects. We provide su¢ cient conditions on the nonlinearity and the impulse functions that guarantee the existence of at least one solution. Our approach is based on a priori estimates, the method of upper and lower solutions combined with an iterative te...

The mean shift algorithm is a non-parametric and iterative technique that has been used for finding modes of an estimated probability density function. It has been successfully employed in many applications in specific areas of machine vision, pattern recognition, and image processing. Although the mean shift algorithm has been used in many applications, a rigorous proof of its convergence is s...

Abstract In this paper, we introduce a new iterative forward-backward splitting method with an error for solving the variational inclusion problem of sum two monotone operators in real Hilbert spaces. We suggest and analyze under some mild appropriate conditions imposed on parameters such that another strong convergence theorem these is obtained. also apply our main result to improve fast shrin...

We survey some recent results on iterative methods for approximating the least solution of a system of monotone fixed-point polynomial equations.

The purpose of this paper is to provide some remarks for the main results of the paper Verma (Appl. Math. Lett. 21:142-147, 2008). Further, by using the generalized proximal operator technique associated with the (A,η,m)-monotone operators, we discuss the approximation solvability of general variational inclusion problem forms in Hilbert spaces and the convergence analysis of iterative sequence...

Investigation of positive solutions of multipoint second-order ordinary boundary value problems, initiated by Il’in and Moiseev [1, 2], has been extensively addressed by many authors, for instance, see [3–6]. Multipoint problems refer to a different family of boundary conditions in the study of disconjugacy theory [7]. Recently, Eloe and Ahmad [8] addressed a nonlinear nth-order BVP with nonloc...