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The inequality of Karisti and generalized compression (the case of singular images)

Annotation

In the present paper we consider a new inequality of Carity type and prove a theorem on a fixed point. Further, relying on the theorem obtained, we study maps (generalized contractions) that compress relative to some function of two vector arguments. This function does not need to be a metric or even continuous.

Keywords

metric space; generalized compression; fixed point

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DOI

10.20310/1810-0198-2018-23-122-243-249

UDC

517.988.6

Pages

243-249

References

1. Bessaga C. On the convers of the Banach fixed point principle. Colloc. Math., 1959, vol. 7, no. 1, pp. 41-43. 2. Ivanov A.A. Nepodvizhnye tochki otobrazheniy metricheskikh prostranstv [Fixed points of mappings of metric spaces]. Zapiski nauchnogo seminara LOMI – Journal of Soviet Mathematics, 1976, vol. 66, pp. 5-102. (In Russian). 3. Dugundji J., Granas A. Fixed point theory. Warszawa, PWN, 1982. 4. Oben Zh.-P. Nelineynyy analiz i ego ekonomicheskie prilozheniya [Nonlinear Analysis and Its Economic Applications]. Moscow, Mir Publ., 1988. (In Russian). 5. Arutyunov A.V. Uslovie Karisti i sushchestvovanie minimuma ogranichennoy snizu funktsii v metricheskom prostranstve. Prilozheniya k teorii tochek sovpadeniya [Caristi’s condition and existence of a minimum of a lower bounded function in a metric space. Applications to the theory of coincidence points]. Trudy matematicheskogo instituta im. V.A. Steklova – Proceedings of the Steklov Institute of Mathematics, 2015, vol. 291, pp. 30-44. (In Russian). 6. Nemytskiy V.V. Metod nepodvizhnykh tochek v analize [The method of fixed points in the analysis]. Uspekhi matematicheskih nauk – Russian Mathematical Surveys, 1936, no. 1, pp. 141-174. (In Russian).

Received

2018-03-21

Section of issue

Scientific articles

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