On the convergence of a modified superquadratic method for generalized equations

Mohammed Harunor Rashid; Md. Zulfiker Ali

doi:10.32323/ujma.415225

EN

On the convergence of a modified superquadratic method for generalized equations

Abstract

Let $X$ and $Y$ be Banach spaces. Let $\Omega$ be an open subset of $X$. Suppose that $f:X\to{Y}$ is Fr\'{e}chet differentiable in $\Omega$ and $\mathcal F:X\rightrightarrows2^Y$ is a set-valued mapping with closed graph. In the present paper, a modified superquadratic method (MSQM) is introduced for solving the generalized equations $0\in{f(x)+\mathcal F(x)}$, and studied its convergence analysis under the assumption that the second Fr\'{e}chet derivative of $f$ is H\"{o}lder continuous. Indeed, we show that the sequence, generated by MSQM, converges super-quadratically in both semi-locally and locally to the solution of the above generalized equation whenever the second Fr\'{e}chet derivative of $f$ satisfies a H\"{o}lder-type condition.

Keywords

Generalized equations,Lipschitz--like mappings,Semi-local convergence,Set-valued mapping

References

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Mohammed Harunor Rashid ^*
0000-0001-8537-1596
Bangladesh

Md. Zulfiker Ali This is me
Bangladesh

Publication Date

September 30, 2018

Submission Date

April 14, 2018

Acceptance Date

September 16, 2018

Published in Issue

Year 2018 Volume: 1 Number: 3

DOI

https://doi.org/10.32323/ujma.415225

IZ

https://izlik.org/JA86CL45YR

APA

Rashid, M. H., & Ali, M. Z. (2018). On the convergence of a modified superquadratic method for generalized equations. Universal Journal of Mathematics and Applications, 1(3), 202-214. https://doi.org/10.32323/ujma.415225

AMA

1.Rashid MH, Ali MZ. On the convergence of a modified superquadratic method for generalized equations. Univ. J. Math. Appl. 2018;1(3):202-214. doi:10.32323/ujma.415225

Chicago

Rashid, Mohammed Harunor, and Md. Zulfiker Ali. 2018. “On the Convergence of a Modified Superquadratic Method for Generalized Equations”. Universal Journal of Mathematics and Applications 1 (3): 202-14. https://doi.org/10.32323/ujma.415225.

EndNote

Rashid MH, Ali MZ (September 1, 2018) On the convergence of a modified superquadratic method for generalized equations. Universal Journal of Mathematics and Applications 1 3 202–214.

IEEE

[1]M. H. Rashid and M. Z. Ali, “On the convergence of a modified superquadratic method for generalized equations”, Univ. J. Math. Appl., vol. 1, no. 3, pp. 202–214, Sept. 2018, doi: 10.32323/ujma.415225.

ISNAD

Rashid, Mohammed Harunor - Ali, Md. Zulfiker. “On the Convergence of a Modified Superquadratic Method for Generalized Equations”. Universal Journal of Mathematics and Applications 1/3 (September 1, 2018): 202-214. https://doi.org/10.32323/ujma.415225.

JAMA

1.Rashid MH, Ali MZ. On the convergence of a modified superquadratic method for generalized equations. Univ. J. Math. Appl. 2018;1:202–214.

MLA

Rashid, Mohammed Harunor, and Md. Zulfiker Ali. “On the Convergence of a Modified Superquadratic Method for Generalized Equations”. Universal Journal of Mathematics and Applications, vol. 1, no. 3, Sept. 2018, pp. 202-14, doi:10.32323/ujma.415225.

Vancouver

1.Mohammed Harunor Rashid, Md. Zulfiker Ali. On the convergence of a modified superquadratic method for generalized equations. Univ. J. Math. Appl. 2018 Sep. 1;1(3):202-14. doi:10.32323/ujma.415225