Perturbación y puntos cero para ecuaciones con mapeo acumulativo en espacios normados difusos
Palabras clave:
operador acumulativo, método iterativo, teorema del punto fijo, mapeo no expansivo, punto cero
Resumen
El propósito de este artı́culo es investigar las perturbaciones 1-conjunto contractivas de operadores acumulativos y discutir la solución de un tipo especial de ecuaciones de operadores en espacios normados difusos. También, estudiaremos las perturbaciones y existencia de problemas de puntos cero para ecuaciones no lineales con mapeo acumulativo en espacios normados difusos.
Citas
Amann, H., A note on degree theory for gradient maps, Proc. Amer. Math. Soc. 85, 591–595,
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.
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.
Publicado
2019-06-29
Cómo citar
Rashid, M. H. M., & Al-kasasbeh, F. (2019). Perturbación y puntos cero para ecuaciones con mapeo acumulativo en espacios normados difusos. Divulgaciones Matemáticas, 20(1), 49-66. Recuperado a partir de https://produccioncientificaluz.org/index.php/divulgaciones/article/view/36621
Sección
Artículos de Investigación
