i-manager Publications

Common Fixed Point Results in Fuzzy Metric Spaces with Applications in Dynamic Programming

0*, Shailesh Dhar Diwan**

* Department of Mathematics, Shri Shankaracharya Institute Of Professional Management And Technology, Raipur, Chhattisgarh, India.

** Department of Mathematics, Government Engineering College, Raipur, Chhattisgarh, India.

Periodicity:January - June'2020
DOI : https://doi.org/10.26634/jmat.9.1.17585

Abstract

In this paper we propose several common fixed point theorems for self mappings satisfying CLR_g or CLR_ST properties and weak compatibility in FMS (fuzzy metric spaces). Next, we provide some examples to support our results. Furthermore, as an application of our results we present some system of functional equations that arises in dynamic programming and prove the existence of solutions of such equations and uniqueness of the solutions of such functional equations.

Keywords

FMS (Fuzzy Metric Spaces), (E. A) Property, T - Norm, Weakly Compatible Mappings, T - Conorm, CLR Property, G CLR Property.

How to Cite this Article?

Sharma, P., and Diwan, S. D. (2020). Common Fixed Point Results in Fuzzy Metric Spaces with Applications in Dynamic Programming. i-manager's Journal on Mathematics, 9(1), 38-48. https://doi.org/10.26634/jmat.9.1.17585

References

[1]. Aamri, M., & El Moutawakil, D. (2002). Some new common fixed point theorems under strict contractive conditions. Journal of Mathematical Analysis and Applications, 270(1), 181-188.

[2]. Ali, J., Imdad, M., & Bahuguna, D. (2010). Common fixed point theorems in Menger spaces with common property (EA). Computers & Mathematics with Applications, 60(12), 3152-3159. https://doi.org/10.1016/j.camwa.2010.10.020

[3]. Baskaran, R., & Subrahmanyam, P. (1986). A note on the solution of a class of functional equations. Applicable Analysis, 22(3-4), 235-241.

[4]. Bellman, R. (1957). Dynamic programming. Princeton, New Jersey: Princeton University Press.

[5]. Bellman, R., & Lee, E. S. (1978). Functional equations in dynamic programming. Aequationes Mathematicae, 17(1), 1-18.

[6]. Bhakta, P. C., & Mitra, S. (1984). Some existence theorems for functional equations arising in dynamic programming. Journal of Mathematical Analysis and Applications, 98(2), 348-362.

[7]. Chang, S. S., & Ma, Y. H. (1991). Coupled fixed points for mixed monotone condensing operators and an existence theorem of the solutions for a class of functional equations arising in dynamic programming. Journal of Mathematical Analysis and Applications, 160(2), 468-479.

[8]. Chen, S., Shi, P., & Lim, C. C. (2017). Curve arc length in fuzzy metric spaces. Fuzzy Sets and Systems, 313, 105-113.

[9]. García, J. G., Rodríguez-López, J., & Romaguera, S. (2018). On fuzzy uniformities induced by a fuzzy metric space. Fuzzy Sets and Systems, 330, 52-78.

[10]. George, A., & Veeramani, P. (1994). On some results in fuzzy metric spaces. Fuzzy Sets and Systems, 64(3), 395-399.

[11]. Gregori, V., & Sapena, A. (2002). On fixed-point theorems in fuzzy metric spaces. Fuzzy Sets and Systems, 125(2), 245- 252.

[12]. Gregori, V., Miñana, J. J., & Miravet, D. (2020). Contractive sequences in fuzzy metric spaces. Fuzzy Sets and Systems, 379, 125-133.

[13]. Imdad, M., Pant, B., & Chauhan, S. (2012). Fixed point theorems in menger spaces using the CLRST property and applications. Journal of Nonlinear Analysis and Optimization: Theory & Applications, 3(2), 225-237.

[14]. Jungck, G. (1986). Compatible mappings and common fixed points. International Journal of Mathematics and Mathematical Sciences, 9, 771-779.

[15]. Jungck, G. (1976). Commuting mappings and fixed points. The American Mathematical Monthly, 83, 261-263.

[16]. Jungck, G., & Rhoades, B. E. (2006). Fixed point Theorems for occasionally weakly compatible mappings. Fixed Point Theory, 7, 286-296.

[17]. Kramosil, I., & Michálek, J. (1975). Fuzzy metrics and statistical metric spaces. Kybernetika, 11(5), 336-344.

[18]. Miheţ, D. (2010). Fixed point theorems in fuzzy metric spaces using property EA. Nonlinear Analysis: Theory, Methods & Applications, 73(7), 2184-2188.

[19]. Pant, R. P. (1994). Common fixed points of non-commuting mappings. Journal of Mathematical Analysis and Applications, 188, 436-440.

[20]. Schweizer, B., & Sklar, A. (1960). Statistical metric spaces. Pacific Journal of Mathematics, 10(1), 313-334.

[21]. Sessa, S. (1982). On a weak commutativity condition of mappings in fixed point considerations. Publications de l'Institut Mathématique, 32(46), 149-153.

[22]. Sintunavarat, W., & Kumam, P. (2011). Common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces. Journal of Applied Mathematics. https://doi.org/10.1155/2011/637958

[23]. Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338-353.

[24]. Zheng, D., & Wang, P. (2019). Meir–Keeler theorems in fuzzy metric spaces. Fuzzy Sets and Systems, 370, 120-128.

If you have access to this article please login to view the article or kindly login to purchase the article

Single Article

	North Americas,UK, Middle East,Europe		India	Rest of world
	USD	EUR	INR	USD-ROW
Online	15	15

ADD TO CART

Options for accessing this content:

If you would like institutional access to this content, please recommend the title to your librarian.
If you already have i-manager's user account: Login above and proceed to purchase the article.
New Users: Please register, then proceed to purchase the article.