Perturbations and zero points for equations with accretive mappings in fuzzy normed spaces
Keywords:
accretive operator, iterative method, fixed point theorem, nonexpansive mapping, zero point
Abstract
The purpose of this paper is to investigate the 1-set-contractive perturbations of accretive operators and discuss the solution of a special type of operator equations in fuzzy normed spaces. Also we shall study the perturbations, and the existence, problems of zero points for nonlinear equations with accretive mappings in fuzzy normed spaces.
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PN-space (II), Bull. austral. math. Soc. 73, 169–173, 2006.
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1982.
[2] Amann, H. and Weiss, S., On the uniqueness of the topological degree, Math. Z. 130 (1),
39–54, 1973.
[3] Bag, T. and Samanta, S.K., Fuzzy bounded linear spaces, Fuzzy Sets and Systems. 151,
513–547, 2005.
[4] Barbu, V., Nonlinear semigroup and differential equations in Banach spaces, Edut. Acad.
R.S.R., Bucureesti, 1976.
[5] Browder, F.E. and Nussbaum,R.D., The topological degree for noncompact nonlinear map-
pings in Banach spaces, Bull. Amer. Math. Soc. 74 , 671–676, 1968.
[6] Chang, S. S. and Chen, Y. Q., On the existence of solutions for equations with accretive
mappings in PN-spaces, Appl. Math. Mech. 11(9), 821–828, 1990.
[7] Chang, S. S. and Chen, Y. Q., Topological degree theory and fixed point theorems in proba-
bilistic metric spaces, Appl. Math. Mech. 10(6), 495–505, 1989.
[8] Chang, S. S. Cho, Y. J. and Kang, S. M., Nonlinear Operator Theory in Probabilistic Metric
Spaces, Nova Science Publishers Inc, New York, 2001.
[9] J. Dugundji, An extension of Tietze’s theorem, Pacific J. Math. 1, 353–367, 1951.
[10] Ha, K. S., Shin, K. Y. and Cho, Y. J., Accretive operators in probabilistic normed spaces,
Bull. Korean Math. Soc. 31 (1), 45–54, 1994.
[11] Huang, X. Q., Wang, M. S. and Zhu, C. X., The topological degree of A-proper mapping in
the Menger PN-space (I), Bull. Aust. Math. Soc. 73, 161–168, 2006.
[12] Li, G. Z., Xu, S. Y. and Duan, H. G., Fixed point theorems of 1-set-contractive operators in
Banach spaces, Appl. Math. Lett. 19(5),403–412, 2006.
[13] Nǎdǎban, S. and Dzitac, I., Atomic Decomposition of fuzzy normed linear spaces for wavelet
applications, Informatica 25(4), 643–662, 2014.
[14] Schweizer, B. and Sklar, A., Statistical metric spaces, Pacific J. Math. 10, 313–334, 1960.
[15] Schweizer, B. and Sklar, A., Probabilistical Metric Spaces, Dover Publications, New York,
2005.
[16] Sherwood, H., On the completion of probabilistic metric spaces, Wahrscheinlichkeitstheorie
verw Gebiete 6, 62–64, 1966.
[17] Wardowski, D., Fuzzy contractive mappings and fixed points in fuzzy metric spaces, Fuzzy
Sets and Systems, 222, 108–114, 2013.
[18] Wu, Z. Q. and Zhu, C. X., Topological degree for 1-set-contractive fields in M-PN spaces and
its applications, Appl. Math. J. Chin. Univ. 25(4), 463–474, 2010.
[19] Xu, S. Y., New fixed point theorems for 1-set-contractive operators in Banach spaces, Non-
linear Anal. 67(3), 938–944, 2007.
[20] C. X. Zhu, Some new fixed point theorems in probabilistic metric spaces, Appl. Math. Mech.
16(2), 179–185, 1995.
[21] Zhu, C. X., Several nonlinear operator problems in the Menger PN space, Nonlinear Anal.
65, 1281–1284, 2006.
[22] Zhu, C. X., Research on some problems for nonlinear operators, Nonlinear Anal. 71(10),
4568– 4571, 2009.
[23] Zhu, C. X. and Huang, X. Q., The topological degree of A-proper mapping in the Menger
PN-space (II), Bull. austral. math. Soc. 73, 169–173, 2006.
[24] Zeng, W. Z., Probabilistic contractor and nonlinear equation in Menger PN-spaces, J. Math.
Research Expos. 11, 47–51, 1991.
[25] Zhu, C. X. and Xu, Z. B., Inequalities and solution of an operator equation, Appl. Math.
Lett. 21 (6), 607–611, 2008.
[26] Zhu, J., Wang Y. and Zhu, C. C., Fixed point theorems for contractions in fuzzy normed
spaces and intuitionistic fuzzy normed spaces, Fixed Point Theory Appl. 2013 2013:79 DOI:
10.1186/1687-1812-2013-79.
Published
2019-06-29
How to Cite
Rashid, M. H. M., & Al-kasasbeh, F. (2019). Perturbations and zero points for equations with accretive mappings in fuzzy normed spaces. Divulgaciones Matemáticas, 20(1), 49-66. Retrieved from https://www.produccioncientificaluz.org/index.php/divulgaciones/article/view/36621
Section
Research papers
