The Banach Fixed Point Theorem for mappings in general (< R,Ro >,φ)-spaces

  • Andrzej Mach Education Faculty of Engineering and Economics Department of Informatics, The State Higher School of Vocat. Narutowicza 906-400 Ciechanow, Poland
Keywords: Fixed point, binary relation, I-transitivity, contraction, Banach fixed point theorem, (R, I)-space, general (< R, R0 > I)-space, < R, R0 >-contraction.

Abstract

The paper includes theorem giving the sufficient condition to the existence of a fixed point for mappings in arbitrary set equipped with the the family of binary reflexive and symmetric relations satisfying some conditions. The result obtained is a generalization of the main theorem from [7].

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References

S. Banach, Sur les opération dans l'ensembles abstraits et leur application aux équations intégrales, Fundam. Math. 3 (1922), 133-181.

J. Dugundji and A. Granas, Fixed Point Theory, Monograe Matematyczne, Tom 61 vol. I, PWN- Polish Scientic Publishers (1982).

S. K. Chatterjea, Fixed-points theorems, C. R. Acad. Bulgare Sci.,

(1972), 727-730.

J. Jachymski, Common fixed point theorems for some families of mappings, Indian J. Pure Appl. Math., 25 (1994), 925-937.

K. Jha, R. P. Pant, S. L. Singh, Common xed points for comapatible

mappings in metric spaces, Radovi Matemati£ki, vol. 12 (2003), 107-114.

R. Kannan, Some results on xed points II, Am. Math. Mon., 76(4) (1969), 405-408.

A. Mach, A generalization of Banach Fixed Point Theorem for mappings in (R; ')-spaces, International Mathematical Forum, Vol. 10, 2015, no. 12, 579-585.

A. Mach, Some theorem on common xed points and points of coincidence for mappings in metric space, Journal of Progressive Research in Mathematics, Vol.7 No 1, (2016), 892-898.

A. Mach, Chaterjea type condition for existence of common xed point

for 2n + 1 mappings in metric space, Journal of Progressive Research in

Mathematics, Vol.7 No 4, (2016), 1102-1108.

R. P. Pant, P. C. Joshi, V. Gupta, A Meir-Keeler type fixed point theorem, Indian J. Pure Appl. Math., 32(6) (2001), 779-787.

Published
2017-07-14
How to Cite
Mach, A. (2017). The Banach Fixed Point Theorem for mappings in general (< R,Ro &gt;,φ)-spaces. Journal of Progressive Research in Mathematics, 12(2), 1828-1833. Retrieved from http://scitecresearch.com/journals/index.php/jprm/article/view/1167
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