Abstract
In this paper we prove existence and uniqueness of a common fixed point for non-self coincidentally commuting mappings with nonlinear, generalized contractive condition defined on strictly convex Menger PM-spaces proved.
Acknowledgement
For the first and third author this research is supported by the Ministry of Education, Science and Technological Development of Republic of Serbia, institutionally funded through the Faculty of Mathematics, University of Belgrade (for the first author) and through the School of Electrical Engineering, University of Belgrade (for the third author). Authors would like to thank to the reviewer for useful comments.
(Communicated by Anatolij Dvurečenskij)
References
[1] ASSAD, N. A.—KIRK, W. A.: Fixed-point theorems for set-valued mappings of contractive type Pacific J. Math. 43 (1972), 553-562.10.2140/pjm.1972.43.553Suche in Google Scholar
[2] BOYD, D. W.—WONG, J. S. W.: On nonlinear contractions Proc. Amer. Math. Soc. 20 (1969), 458-464.10.1090/S0002-9939-1969-0239559-9Suche in Google Scholar
[3] BROWDER, F. E.: On the convergence of successive approximations for nonlinear functional equations Indag. Math. 30(1) (1968), 27-35.10.1016/S1385-7258(68)50004-0Suche in Google Scholar
[4] ĆIRIĆ, L. B.: On fixed point of generalized contractions on probabilistic metric spaces Publ. Inst. 18(32) (1975), 71-78.Suche in Google Scholar
[5] EGBERT, R. J.: Products and quotients of probabilistic metric spaces Pacific J. Math. 24 1968, 437-455.10.2140/pjm.1968.24.437Suche in Google Scholar
[6] FURI, M.—VIGNOLI, A.: A fixed point theorem in complete metric spaces Boll. Unione Mat. Ital. 2(4-5) (1969), 505-509.Suche in Google Scholar
[7] GAJIĆ, L.—RAKOČEVIĆ. Pair of non-self-mappings and common fixed points Appl. Math. Comput. 187 (2007), 999-1006.10.1016/j.amc.2006.09.143Suche in Google Scholar
[8] HADŽIĆ, O.: Common fixed point theorems in probabilistic metric spaces with a convex structure Zb. Rad. Prirod. - Mat. Fak. Ser. Mat. 18 (1987), 165-78.Suche in Google Scholar
[9] IMDAD, M.—KHAN, L.: Some common fixed point theorems for family of mappings in metrically convex spaces Nonlinear Anal. 67 (2007), 2717-2726.10.1016/j.na.2006.09.037Suche in Google Scholar
[10] IMDAD, M.—KUMAR, S.: Rhoades type fixed-point theorems for a pair of nonself mappings Comput. Math. Appl. 46 (2003), 919-927.10.1016/S0898-1221(03)90153-2Suche in Google Scholar
[11] JEŠIĆ, S. N.: Convex structure, normal structure and a fixed point theorem in intuitionistic fuzzy metric spaces Chaos Solitons Fractals 41 (2008), 292-301.10.1016/j.chaos.2007.12.002Suche in Google Scholar
[12] JEŠIĆ, S. N.—NIKOLIĆ, R. M.—BABAČEV, N. A.: A common fixed point theorem in strictly convex Menger PM-spaces Filomat 28(4) (2014), 735-743.10.2298/FIL1404735JSuche in Google Scholar
[13] JEŠIĆ, S. N.—NIKOLIĆ, R. M.—PANT, R. P.: Common fixed point theorems for self-mappings in Menger PM-spaces with nonlinear contractive condition J. Fixed Point Theory Appl. 20(90) (2018), 2-11.10.1007/s11784-018-0569-7Suche in Google Scholar
[14] JEŠIĆ, S. N.—O’REGAN, D.—BABAČEV, N. A.: A common fixed point theorem for R-weakly commuting mappings in probabilistic spaces with nonlinear contractive conditions Appl. Math. Comput. 1f2 (2008), 272-281.10.1016/j.amc.2007.12.020Suche in Google Scholar
[15] MENGER, K.: Statistical metric Proc. Nat. Acad. Sci. 28 (1942), 535-537.10.1007/978-3-7091-6045-9_35Suche in Google Scholar
[16] RHOADES, B. E.: A fixed point theorem for some non-self mappings Math. Japon. 23 (1978), 457-459.Suche in Google Scholar
[17] SCHWEIZER, B.—SKLAR, A.: Statistical metric spaces Pacific J. Math. 10 (1960), 415-417.10.2140/pjm.1960.10.313Suche in Google Scholar
[18] SCHWEIZER, B.—SKLAR, A.: Probabilistic Metric Spaces North-Holland, New York. Elsevier, 1983.Suche in Google Scholar
[19] SEGHAL, V. M.—BHARUCHA-REID, A. T.: Fixed points of contraction mappings in PM-spaces Math. System Theory 6 (1972), 97-102.10.1007/BF01706080Suche in Google Scholar
[20] SHERWOOD, H.: Complete probabilistic metric spaces Z. Wahrsch. Verw. Gebiete 20 (1971), 117-128.10.1007/BF00536289Suche in Google Scholar
[21] TAKAHASHI, W.: A convexity in metric space and nonexpansive mappings Kodai Math. Sem. Rep. 22 (1970), 142-149.10.2996/kmj/1138846111Suche in Google Scholar
[22] ZITAROSA, A.: Una generalizzazione del teorema di Banach sulle contrazioni Matematiche 23(2) (1968), 417-424.Suche in Google Scholar
© 2020 Mathematical Institute Slovak Academy of Sciences
Artikel in diesem Heft
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- The lattices of 𝔏-fuzzy state filters in state residuated lattices
- Central lifting property for orthomodular lattices
- EQ-Modules
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- Divisible extension of probability
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Artikel in diesem Heft
- Regular papers
- Fuzzy deductive systems of RM algebras
- Congruence pairs of principal MS-algebras and perfect extensions
- The lattices of 𝔏-fuzzy state filters in state residuated lattices
- Central lifting property for orthomodular lattices
- EQ-Modules
- On the exponential Diophantine equation Pxn + Pxn+1 + ⋯ + Pxn+k-1 = Pm
- Remarks on some generalization of the notion of microscopic sets
- Disjointness of composition operators on Hv0 spaces
- A common fixed point theorem for non-self mappings in strictly convex menger PM-spaces
- The Poincaré-Cartan forms of one-dimensional variational integrals
- Coarse cohomology with twisted coefficients
- Divisible extension of probability
- Asymptotic behavior of the records of multivariate random sequences in a norm sense
- Strong convergence of the functional nonparametric relative error regression estimator under right censoring
- A new kumaraswamy generalized family of distributions: Properties and applications
- Efficient message transmission via twisted Edwards curves
- Computation of several Hessenberg determinants