The N-fuzzy metric spaces and mappings with application

• Autorzy: Malviya N.

Identyfikatory

DOI

10.1515/fascmath-2015-0019

• Języki publikacji: EN

Abstrakty

EN

In the present paper, we introduce the notion of N-fuzzy metric spaces (NFMS_s), Pseudo N-fuzzy metric spaces and describe some of their properties. Also we prove a fixed point theorem using implicit relation in N-fuzzy metric spaces.

Słowa kluczowe

EN

N-fuzzy metric space; pseudo-N-fuzzy metric space; fixed point; compatible maps; weak compatible maps; semicompatible maps; property (E.A.)

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2015
• Tom: Nr 55
• Strony: 133--151
• Opis fizyczny: Bibliogr. 29 poz.

Twórcy

autor

Malviya N.

• NRI Institute of Information Science and Technology Bhopal, India

Bibliografia

• [1] Aalam I., Kumar S., Pant B.D., A common fixed point theorem in fuzzy metric space, Bulletin of Mathematical Analysis and Applications, 2(4)(2010), 76-82.
• [2] Abbas M., Altun I., Gopal D., Common fixed point theorems for non compatible mappings in fuzzy metric spaces, Bulletin of Mathematical Analysis and Applications, 1(2)(2009), 47-56.
• [3] An T.V., Dung N.V., Kadelburg Z., Radenović S., Various generalizations of metric spaces and fixed point theorems, Re vista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas (RACSAM), DOI 10.1007/s13398-014-0173-7.
• [4] Chauhan S., Radenović S., Bhatnagar S., Common fixed point theorems for weakly compatible mappings in fuzzy metric spaces, Le Mathematiche, LXVIII (2013)-Fasc. I, 87-98 D0I:10.4418/2013.68.1.8.
• [5] Chauhan S., Radenović S., Imdad M., Vetro C., Some integral type fixed point theorems in non-archimedean menger PM-spaces with common property (E.A) and applications of functional equations in dynamic programming, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales, Serie A. Matematicas (RACSAM), 2013, DOI: 10.1007/s13398-013-0142-6.
• [6] Chauhan S., Shatanawi W., Kumar S., Radenović S., Existence and uniqueness of fixed points in modified intuitionistic fuzzy metric spaces, J. Nonlinear Sci. Appl., 6(2013), 1-12.
• [7] Dhage B.C., Generalized metric spaces and mapping with fixed points, Bulletin of the Calcutta Mathematical Society, 84(1992), 329-336.
• [8] Došenović T., Rakić D., Carić B., Radenović S., Multivalued generalizations of fixed point results in fuzzy metric spaces, Nonlinear Analysis: Modelling and Control., (accepted for printing).
• [9] Gahlers S., 2-metrische Raume and ihre topologische structure, Math.Nachr, 26(1963), 115-148.
• [10] Gahlers S., Zur geometric 2-metrische raume, Revue Roumaine Math.Pures Appl., 11(1966), 665-667.
• [11] George A., Veeramani P., On some results in fuzzy metric spaces, Fuzzy Sets Syst., 64(1994), 395-399.
• [12] Ha K.S., Cho Y.J., White A., Strictly convex and strictly 2-convex 2-normed spaces, Mathematica Japonica, 33(3)(1988), 375-384..
• [13] Hadžić O., On the (ϵ, λ) topology of probabilistic locally convex spaces, Glasnik Matematicki III, 13(33)(1978), 293-297.
• [14] Kramosil O., Michalek J., Fuzzy metrics and statistical metric spaces, Kybernetika, 11(1975), 326-334.
• [15] Kumar S., Common fixed point theorem in fuzzy 2-metric spaces, Uni.Din. Bacau. Studii Si Cercetiri Sciintifice, Serial: Mathematical, 18(2008), 111-116.
• [16] Mustafa Z., Sims B., Some remarks concerning D-metric space, International Conference on Fixed Point Theory and Applications, Valencia, Spain, (2003), 189-198.
• [17] Mustafa Z., Sims B., A new approach to generalized metric spaces, Journal of Nonlinear and Convex Analysis, 7(2)(2006), 289-297.
• [18] Pathak H.K., Rodriguez-Lopez R., Verma R.K., A common fixed point theorem using implicit relation and property (E.A.) in metric spaces, Filomat, 21(2)(2007), 211-324.
• [19] Radenović S., Kadelburg Z., Jandrlić D., Jandrlić A., Some results on weakly contractive maps, Bulletin of the Iranian Mathematical Society, 38(3)(2012), 625-645.
• [20] Rao K.P.R., Altun I., Hina Bindu S., Common coupled fixed point theorems in generalized fuzzy metric spaces, Advances in Fuzzy Systems, 2011 Article ID 986748, 6 Pages.
• [21] Schweizer B., Sklar A., Satatistical metric space, Pacific J. Math., 10(1)(1960), 313-334.
• [22] Sedghi S., Shobe N., Fixed point thoerems in M -fuzzy metric spaces with property (E), Advances in Fuzzy Mathematics, 1(1)(2006), 55-65.
• [23] Sedghi S., Shobe N., A common fixed point theorem in two M-fuzzy metric space, Commun, Korean. Math. Soc., 22(4)(2007), 513-526.
• [24] Sedghi S., Shobe N., Aliouche A., A generalization of fixed point theorems in S-metric spaces, Mat. Vesnik, 64(3)(2012), 258-266.
• [25] Sedghi S., Shobe N., Zhou H., A common fixed point theorem in D*-metric spaces, Fixed Point Theory and Application, (2007), Article ID 27906, 13 pages.
• [26] Sharma S., On fuzzy metric space, Southeast Asian Bulletin of Mathematics, 26(2002), 133-145.
• [27] Singh B., Chauhan M.S., Generalized fuzzy metric spaces and fixed point theorems, Bull, Cal. Math. Soc., 89(1997), 457- 460.
• [28] Singh B., Jain S., Semicompatibility and fixed point theorems in fuzzy metric space using implicit relation, International Journal of Mathematics and Mathematical Sciences, 16(2005), 2617-2629.
• [29] Sun G., Yang K., Generalized fuzzy metric spaces with properties, Research journal of Applied Sciences, Engineering and Technology, 2(7)(2010), 673-678.