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Demonstratio Mathematica

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Strict contractive conditions and common fixed point theorems with application

Autorzy Pant, V.
Treść / Zawartość https://www.degruyter.com/view/j/dema
Warianty tytułu
Języki publikacji EN
Abstrakty
 EN The aim of the present paper is to obtain common fixed point theorems under a strict contractive condition by assuming minimal commutativity conditions. Our theorems extend the results due to Pant and Pant [4]. In the setting of our results, we also provide pair of mappings which ensures the existence of a common fixed point; however, both the mappings are discontinuous at the common fixed point. We, thus, provide one more answer to the problem of Rhoades [10]. In the last section, we apply our results to solve an eigenvalue problem.
Słowa kluczowe
 PL punkt stały   warunek skurczu   mapa niekompatybilna EN common fixed points   contractive condition   conditionally commuting maps   noncompatible map
Wydawca De Gruyter
Czasopismo Demonstratio Mathematica
Rocznik 2013
Tom Vol. 46, nr 2
Strony 405--413
Opis fizyczny Bibliogr. 10 poz.
Twórcy
 autor Pant, V. DA - 81 F, Hari Nagar, New Delhi - 110064, India, vyomeshpant@yahoo.co.in
Bibliografia
[1] M. Aamri, D. El. Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl. 270 (2002), 181–188.
[2] A. R. Khan, A. A. Domlo, Common Fixed Points of Weekly Compatible Maps on Balls and Applications, Technical Report Series, TR 336, October 2005, King Fahd University of Petroleum and Minerals.
[3] G. Jungck, Compatible mappings and common fixed points, Internat. J. Math. Sci. 9 (1986), 771–779.
[4] R. P. Pant, V. Pant, Common fixed point under strict contractive conditions, J. Math. Anal. Appl. 248 (2000), 327–332.
[5] R. P. Pant, V. Pant, K. Jha, Note on common fixed point under strict contractive conditions, J. Math. Anal. Appl. 274 (2002), 879–880.
[6] R. P. Pant, Common fixed points of noncommuting mappings, J. Math. Anal. Appl. 188 (1994), 436–440.
[7] R. P. Pant, Discontinuity and fixed points, J. Math. Anal. Appl. 240 (1999), 284–289.
[8] V. Pant, R. P. Pant, Common fixed points of conditionally commuting maps, Fixed Point Theory 11(1) (2010), 113–118.
[9] H. K. Pathak, Y. J. Cho, S. M. Kang, Remarks on R-weakly commuting mappings and common fixed point theorems, Bull. Korean Math. Soc. 34 (1997), 247–257.
[10] B. E. Rhoades, Contractive definitions and continuity, Contemp. Math. 72 (1988), 233–245.
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