A new class of nonexpansive type mappings and fixed points

Ljubomir B. Ćirić

Czechoslovak Mathematical Journal (1999)

  • Volume: 49, Issue: 4, page 891-899
  • ISSN: 0011-4642

Abstract

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In this paper a new class of self-mappings on metric spaces, which satisfy the nonexpensive type condition (3) below is introduced and investigated. The main result is that such mappings have a unique fixed point. Also, a remetrization theorem, which is converse to Banach contraction principle is given.

How to cite

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Ćirić, Ljubomir B.. "A new class of nonexpansive type mappings and fixed points." Czechoslovak Mathematical Journal 49.4 (1999): 891-899. <http://eudml.org/doc/30533>.

@article{Ćirić1999,
abstract = {In this paper a new class of self-mappings on metric spaces, which satisfy the nonexpensive type condition (3) below is introduced and investigated. The main result is that such mappings have a unique fixed point. Also, a remetrization theorem, which is converse to Banach contraction principle is given.},
author = {Ćirić, Ljubomir B.},
journal = {Czechoslovak Mathematical Journal},
keywords = {nonexpansive type mapping; asymptotically regular mapping; fixed point; nonexpansive type mapping; asymptotically regular mapping; fixed point},
language = {eng},
number = {4},
pages = {891-899},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A new class of nonexpansive type mappings and fixed points},
url = {http://eudml.org/doc/30533},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Ćirić, Ljubomir B.
TI - A new class of nonexpansive type mappings and fixed points
JO - Czechoslovak Mathematical Journal
PY - 1999
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 49
IS - 4
SP - 891
EP - 899
AB - In this paper a new class of self-mappings on metric spaces, which satisfy the nonexpensive type condition (3) below is introduced and investigated. The main result is that such mappings have a unique fixed point. Also, a remetrization theorem, which is converse to Banach contraction principle is given.
LA - eng
KW - nonexpansive type mapping; asymptotically regular mapping; fixed point; nonexpansive type mapping; asymptotically regular mapping; fixed point
UR - http://eudml.org/doc/30533
ER -

References

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  1. 10.4153/CMB-1976-002-7, Canad. Math. Bull 19 (1976), 7–12. (1976) Zbl0329.47021MR0417866DOI10.4153/CMB-1976-002-7
  2. Applications of an extension of a theorem of Fisher on common fixed point, Pure Math. Manuscript 6 (1987), 35–38. (1987) Zbl0664.54029MR0981322
  3. On a common fixed point theorem of a Greguš type, Publ. Inst. Math. (Beograd) (N.S.) 49 (63) (1991), 174–178. (1991) MR1127395
  4. On some discontinuous fixed point mappings in convex metric spaces, Czechoslovak Math. J. 43 (118) (1993), 319–326. (1993) MR1211753
  5. On Diviccaro, Fisher and Sessa open questions, Arch. Math. (Brno) 29 (1993), 145–152. (1993) MR1263115
  6. Nonexpansive type mappings and fixed point theorems in convex metric spaces, Rend. Accad. Naz. Sci. XL Mem. Mat. (5), Vol. XIX (1995), 263–271. (1995) 
  7. On some nonexpansive type mappings and fixed points, Indian J. Pure Appl. Math. 24 (3) (1993), 145–149. (1993) MR1210385
  8. On same mappings in metric space and fixed points, Acad. Roy. Belg. Bull. Cl. Sci. (5) T.VI (1995), 81–89. (1995) MR1385507
  9. Teoremi di punto fisso per applicazioni negli spazi di Banach, Boll. Un. Mat. Ital. A. (6) 2 (1993), 297–303. (1993) MR0724481
  10. A common fixed point theorem of Greguš type, Publ. Math. (Debrecen) 34 (1987), 83–89. (1987) MR0901008
  11. A generalized contraction mapping principle and infinite systems of differential equations, Differentsialnye Uravneniya 26 (1990), no. 8, 1299–1309, 1467 (in Russian). (1990) MR1074257
  12. Common fixed points on a Banach space, Chung Yuan J. 11 (1982), 19–26. (1982) 
  13. 10.1155/S0161171286000030, Internat. J. Math. Sci. 9 (1986), 23–28. (1986) MR0837098DOI10.1155/S0161171286000030
  14. A fixed point theorem in Banach spaces, Boll. Un. Mat. Ital. A (5) 17 (1980), 193–198. (1980) 
  15. On common fixed point theorems of mappings, Proc. Japan Acad. Ser. A Math. Sci. 50 (1974), 408–409. (1974) Zbl0312.54045MR0440524
  16. 10.1155/S0161171290000710, Internat. J. Math. Sci. 13 (1990), 497–500. (1990) Zbl0705.54034MR1068012DOI10.1155/S0161171290000710
  17. 10.1007/BF02014826, Appl. Math. Mech. (English Ed.) 10 (1989), 183–188. (1989) DOI10.1007/BF02014826
  18. A converse to Banach’s contraction theorem, J. Res. Nat. Bur. Standards, Sect. B 71 (1967), 73–76. (1967) Zbl0161.19803MR0221469
  19. A note on a fixed point theorem of Greguš, Math. Japon. 33 (1988), 745–749. (1988) MR0972387
  20. A survey of recent applications of fixed point theory to periodic solutions of the Lienard equations, Fixed point theory and its applications, (Berkley, CA 1986), 171–178, Contemp. Math. 72, Amer. Math. Soc., Providence, RI, 1988. (1988) MR0956489
  21. A generalization of a fixed point theorem of Bogin, Math. Sem. Notes, Kobe Univ. 6 (1978), 1–7. (1978) Zbl0387.47040MR0500749
  22. Some applications of contractive type mappings, Math. Sem. Notes, Kobe Univ. 5 (1977), 137–139. (1977) Zbl0362.54044MR0467716
  23. Study of applications of Banach’s fixed point theorem, Chittagong Univ. Stud., Part II Sci. 11 (1987), 85–91. (1987) MR0981206
  24. Applications of fixed point theorems in game theory and mathematical economics (Polish), Wiadom. Mat. 28 (1988), 25–34. (1988) MR0986059

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