SOME COMMON FIXED POINT THEOREMS FOR FUZZY TYPE RATIONAL CONTRACTIVE MAPPINGS IN HILBERT SPACES

R. A. RASHWAN; S. MANRO; S. K. ABDEL-AAL

doi:10.56557/ajocr/2022/v7i27896

SOME COMMON FIXED POINT THEOREMS FOR FUZZY TYPE RATIONAL CONTRACTIVE MAPPINGS IN HILBERT SPACES

R. A. RASHWAN

S. MANRO

S. K. ABDEL-AAL

Asian Journal of Current Research, Page 15-23
DOI: 10.56557/ajocr/2022/v7i27896
Published: 17 October 2022

Abstract

Heilpern [1] introduced and studied the concept of fuzzy mappings and proved some fixed point theorems for fuzzy contraction mappings. Subsequently several authors studied and generalized the existence of fixed points and common fixed points of fuzzy mappings satisfying various contraction type conditions in metric spaces (see [2],[3],[4],[5], and others). Dutta P.N and Choudhury B.S [6] studied some fixed points for fuzzy mappings in Hilbert spaces. Further Shrivastava R. et al. [7] proved a common fixed point theorem for fuzzy type mapping in Hilbert space. Motivated by the results in [6, 7], we prove three common fixed point theorems for fuzzy rational type mappings in Hilbert spaces. The results extend and generalize many previous known results in the literature.

Keywords:

Fuzzy mappings
Hilbert space
fixed points
approximate quantity

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How to Cite

RASHWAN, R. A., MANRO, S., & ABDEL-AAL, S. K. (2022). SOME COMMON FIXED POINT THEOREMS FOR FUZZY TYPE RATIONAL CONTRACTIVE MAPPINGS IN HILBERT SPACES. Asian Journal of Current Research, 7(2), 15-23. https://doi.org/10.56557/ajocr/2022/v7i27896

References

Heilpern S. Fuzzy mappings and fixed point

theorem. Journal of Mathematical Analysis and Applications. 1981;83:566-569.

DOI: 10.1016/0022-247X(81)90141-4

Banciari A. A fixed point theorem for mappings satisfying a general contractive condition of integral type. Int. J. Math. Sci. 2002;29:531-536.

DOI: 10.1155/S0161171202007524

Bose BK, Sahani D. Fuzzy mappings and fixed point theorems. Fuzzy Sets and Systems. 1987;21:53-58.

DOI: 10.1016/0165-0114(87)90152-7

Butnariu D. Fixed points for fuzzy mappings. Fuzzy Sets and Systems. 1982;7:191-207.

DOI: 10.1016/0165-0114(82)90049-5

Chang SS. Fixed point theorems for fuzzy mappings. Fuzzy Sets and Systems. 1985;17:181-187. DOI: 10.1016/0165- 0114(85)90055-7

Dutta PN, Choudhury BS. Fixed points of fuzzy mappings in Hilbert space. Mathematical Communications. 2002;7:91-96.

Shrivastava R, Rajput A, Singh S. A common fixed point theorem for fuzzy type mappings in Hilbert space. Ultra Scientist. 2012;24:255-258. Available:http://www.ultrascientist.org/ 411/download-research-paper

¨ zer O, Shatarah A. An Investigation of the Fixed Point Analysis and Practices. NOVA Science Publisher, New York, U.S.A.; 2021. ISBN: 978-1-53619-565-1.

¨ zer O, Omran S. Common fixed point theorems in C*- algebra valued b-metric spaces. AIP Conference Proceedings 1773, 050005; 2016.DOI: 10.1063/1.4964975

Frasser C, O¨ zer O. First-order ordinary differential equations and applications. Lambert Academic Publishing.

ISBN-13:978-620-2-79841-9, ISBN- 10:6202798416.

Zadeh LA. Fuzzy sets. Inform. Control. 1965;8:338-353.

DOI: 10.1016/S0019-9958(65)90241-X

Deng Z. Fuzzy pseudo-metric spaces. J. Math. Anal. Appl. 1982;86:74-95.

DOI: 10.1016/0022-247X(82)90255-4

Erceg MA. Metric spaces in fuzzy set theory. Journal of Mathematical Analysis and Applications. 1979;69:205-230.

DOI: 10.1016/0022-247X(79)90189-6

Kaleva O, Seikkala S. On fuzzy metric spaces. Fuzzy Sets and Systems. 1984;12:215-229.

DOI: 10.1016/0165-0114(84)90069-1

Kramosil I, Michalek J. Fuzzy metric and statistical metric spaces. Kybernettika. 1975;11:336-344. Available:http://eudml.org/doc/28711

Badard R. Fixed point theorems for fuzzy numbers. Fuzzy Sets and Systems. 1984;13:291-302.

DOI: 10.1016/0165-0114(84)90063-0

Chang SS, Cho YJ, Lee BS, Jung JS, Kang SM. Coincidence point and minimization theorem in fuzzy metric spaces. Fuzzy Sets and Systems. 1997;88:119-128.

DOI: 10.1016/S0165-0114(96)00060-7

Hadzic O. Fixed point theorems for multivalued mappings in some classes of fuzzy metric spaces. Fuzzy Sets and Systems. 1989;29:115-125.

DOI: 10.1016/0165-0114(89)90140-1

Jung JS, Cho YJ, Kim JK. Minimization theorems for fixed point theorems in fuzzy metric spaces and applications. Fuzzy Sets

and Systems. 1994;61:199-207.

DOI: 10.1016/0165-0114(94)90234-8

Rashwan RA, Abdel-Aal SK. Common fixed point theorems for various contraction fuzzy mappings in fuzzy metric spaces. JP Journal of Fixed Point Theory and Applications. 2021;16:77-91.

DOI: 10.17654/fp016230077

Mecheraoui R, Mitrovi´c ZD, Parvaneh V, Aydi H, Saleem N. On some fixed point results in E-fuzzy metric spaces. Journal of Mathematics; 2021.

DOI: 10.1155/2021/9196642

Ekland I, Gahler S. Basic notions for fuzzy topology. Fuzzy Sets and Systems. 1988;26:333-356.

DOI: 10.1016/0165-0114(88)90147-9

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