Strict contractive conditions and common fixed point theorems with application

• Autorzy: Pant V.
• 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

EN

common fixed points; contractive condition; conditionally commuting maps; noncompatible map

PL

punkt stały; warunek skurczu; mapa niekompatybilna

• 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

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.