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Fixed points of generalized Kannan type mappings in generalized Menger spaces

Krishnapada Das|Binayak Samadder Choudhury
대한수학회 (The Korean Mathematical Society)|2009.10|대한수학회논문집 (Communications of the KMS)|제24권 제4호|pp. 529-537

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참고문헌

키워드

fixed pointKannan type mappinggeneralized Menger spaceφ-function
주제분류수학

초록

Generalized Menger space introduced by the present authors is a generalization of Menger space as well as a probabilistic generalization of generalized metric space introduced by Branciari [Publ. Math. Debrecen 57 (2000), no.1-2, 31--37]. In this paper we prove a Kannan type fixed point theorem in generalized Menger spaces. We also support our result by an example.

Abstract

Generalized Menger space introduced by the present authors is a generalization of Menger space as well as a probabilistic generalization of generalized metric space introduced by Branciari [Publ. Math. Debrecen 57 (2000), no.1-2, 31--37]. In this paper we prove a Kannan type fixed point theorem in generalized Menger spaces. We also support our result by an example.

참고문헌 (21)

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  4. B. S. Choudhury, "Banach contraction mapping principle in generalized Menger spaces", ~, (Communicated)
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  10. R. Kannan, "Some results on fixed point II", Amer. Math. Monthly, 76, pp.405~408 (1969)
  11. M. Kikkawa, "Some similarity between contractions and Kannan mappings", Fixed Point Theory and Applications 2008 (2008)
  12. M. Kikkawa, "Some similarity between contractions and Kannan mappings II", Bull. Kyushu Inst. Tech. Pure Appl. Math., (55), pp.1~13 (2008)
  13. I. Kubiaczyk, "Some common fixed point theorems in Menger space under strict contractive conditions", Southeast Asian Bull. Math., 32, pp.117~124 (2008)
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  16. P. K. Saha, "An alternative proof of Kannan’s fixed point theorem in generalized metric space", News Bull. Cal. Math. Soc., 31, pp.15~18 (2008)
  17. B. Schweizer, "Probabilistic Metric Space" (1983), North-Holland
  18. V. M. Sehgal, "Fixed points of contraction mappings on PM space", Math. Sys. Theory, 6(2), pp.97~100 (1972)
  19. Y. Shi, "The extension of fixed point theorems for set valued mapping", J. Appl. Math. & Computing, 13(1), pp.277~286 (2003)
  20. B. Sing, "A fixed point theorem in Menger spaces through weak compatibility", J. Math. Anal. Appl., 301(2), pp.439~448 (2005)
  21. P. V. Subrahmanyam, "Completeness and fixed points", Monatsh. Math., 80, pp.325~330 (1975)

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