Abstract
Abstract In this paper, we introduce a new condition namely, the (W.C.C) condition and give some Suzuki-type, unique, common fixed-point theorems for pairs of hybrid mappings in partial metric spaces using a partial Hausdorff metric. These results generalize and extend the several comparable results in this literature in metric and partial metric spaces.
Highlights
In the case of bounded delays, many authors using standard techniques [3, 10, 20, 27, 34, 37] have studied the asymptotic behavior of solutions, the asymptotic stability in equations and the existence of positive periodic solutions of delay equations
By means of the matrix method based on collocation points which have been given by Sezer and coworkers [2, 6, 16, 17, 21, 26, 29, 36], we develop a novel matrix technique to find the approximate solution of Eq 1 under the initial condition yðaÞ 1⁄4 k in the truncated Morgan–Voyce series form yðtÞ ffi yN ðtÞ 1⁄4
A new approach using the Morgan–Voyce polynomials to solve numerically the first-order nonhomogeneous differential equations with variable delays is presented in this study
Summary
We consider nonhomogeneous differential equation with variable delays in the form [3, 5, 10, 12, 23, 30, 37, 38]. Pj ðtÞy t sj ðtÞ ð1Þ j1⁄42 under the initial condition yðaÞ 1⁄4 k, where the coefficients. Most of the mentioned type delay equations have not analytical and numerical solutions; numerical methods are required to obtain approximate solutions. For this purpose, by means of the matrix method based on collocation points which have been given by Sezer and coworkers [2, 6, 16, 17, 21, 26, 29, 36], we develop a novel matrix technique to find the approximate solution of Eq 1 under the initial condition yðaÞ 1⁄4 k in the truncated Morgan–Voyce series form yðtÞ ffi yN ðtÞ 1⁄4. X 0 ðtÞ 1⁄4 X ðtÞT bo ðtÞ 1⁄4 1; b1 ðtÞ 1⁄4 t þ 1; b2 ðtÞ 1⁄4 t2 þ 3t þ 1; where b3 ðtÞ 1⁄4 t3 þ 5t2 þ 6t þ 1;
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