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

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Published: 2022-10-17

DOI: 10.56557/ajocr/2022/v7i27896

Page: 15-23


R. A. RASHWAN *

Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516, Egypt.

S. MANRO

Department of Mathematics and Computer Applications, Thapar University, Patiala 147004, Punjab, India.

S. K. ABDEL-AAL

Department of Mathematics, Faculty of Science, New Valley University, El-Khargah 72511, Egypt.

*Author to whom correspondence should be addressed.


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


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

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