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Common fixed point theorems using different contractive type conditions involving rational expressions

G. V. R. Babu|M. V. R. Kameswari
장전수학회 (Jangjeon Mathematical Society)|2008.12|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제11권 제2호|pp. 113-136|DOI 10.17777/pjms.2008.11.2.002

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참고문헌

키워드

Metric spacecomplete metric spacecompatible maps of type (A)weakly biased mapsreciprocal continuitycommon fixed points.
주제분류수학

초록

The aim of this paper is to prove some common fixed point theorems for two pairs of selfmaps in complete metric spaces by assuming weak commutativity assumptions like compatible maps of type (A) and weakly biased maps in which the maps satisfy di®erent types of rational contractive conditions. These results improve and extend some of the known results of Fisher [9], Jeong and Rhoades [10].

Abstract

The aim of this paper is to prove some common fixed point theorems for two pairs of selfmaps in complete metric spaces by assuming weak commutativity assumptions like compatible maps of type (A) and weakly biased maps in which the maps satisfy di®erent types of rational contractive conditions. These results improve and extend some of the known results of Fisher [9], Jeong and Rhoades [10].

참고문헌 (18)

  1. G. V. R. Babu, "Weakly biased maps and common fixed point theorems under rational inequality", Advanced Studies in Contemporary Mathematics, 17(1), pp.25~39 (2008), 장전수학회(章田數學會)
  2. Bhagwat, N., "Fixed points of a pair of mappings", Indian J. Pure and Appl. Math, 17, pp.994~997 (1980)
  3. Chatterjea, H., "On generalizations of Banach contraction Principle", Indian. J. of Pure and Appl. Math, 10, pp.400~403 (1979)
  4. Chatterjea, H., "A fixed point theorem in metric spaces, Indian", J. of Pure and Appl. Math, 10(4), pp.449~450 (1979)
  5. Das, P., "Some results on fixed point in complete metric spaces, Indian", J. of Pure and Appl. Math, 13, pp.303~308 (1982)
  6. Dass, B. K., "On extension of Banach contraction principle through rational expression, Indian", J. of Pure and Appl. Math, 6, pp.1455~1458 (1975)
  7. Fisher, B., "Theorems on mappings satisfying a rational inequality", Commentationes Mathematicae Universitatis Carolinae, 19(1), pp.37~44 (1978)
  8. Fisher, B., "Common fixed point and constant mappings satisfying rational inequality", Mathematics Seminar Notes Kobe Univ, 6(1), pp.29~35 (1978)
  9. Fisher, B, "Mappings satisfying rational ineuqality", Nanta. Math, 12 (1979)
  10. Jeong, G. S., "Some remarks for improving ¯xed point theorems for more than two maps", Indian J. Pure and Appl. Math, 24(9), pp.1177~1196 (1997)
  11. Jungck, G., "Compatible mappings and common ¯xed points", Internat. J. Math. Math. Sci, 9(4), pp.771~779 (1986)
  12. Jungck, G., "Compatible mappings of type (A) and common fixed points", Math. Japonica, 38, pp.381~390 (1993)
  13. Jungck, G., "Fixed points via biased maps", Proc. Amer. Math. Soc, 123(7), pp.2049~2059 (1995)
  14. Jungck, G., "Fixed point for set-valued functions without continuity", Indian J. Pure and Appl. Math, 29(3), pp.227~238 (1998)
  15. Mukerjee, R. N., "A generalization of fixed point theorem of Jaggi, Indian", J. Pure and Appl. Math, 14, pp.572~574 (1983)
  16. Pathak, H. K., "Common fixed points of biased maps of type (A) and applications, Internat", J. Math. Math. Sci, 21(4), pp.681~694 (1998)
  17. Renu Chugh, "Fixed points for four mappings", Proc. Indian Acad. Sci. (Math. Sci.), III(29), pp.241~247 (2001)
  18. Rhoades, B. E., "Proving fixed point theorems using general principles", Indian. J. Pure and Appl. Math, 27(8), pp.741~770 (1996)

관련 논문AI추천

Weakly biased maps and common fixed point theorems under rational inequalityG. V. R. Babu, M. V. R. Kameswari장전수학회 · Advanced Studies in Contemporary Mathematics2008 · 제17권 제1호Existence of common ¯xed points for weakly biased maps satisfying weakly contractive condition involving rational expressionsG. N. ALEMAYEHU, G. V. R. BABU장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2011 · 제14권 제1호COMMON FIXED POINTS OF TWO PAIRS OF GENERALIZED WEAKLY CONTRACTIVE MAPSG. N. ALEMAYEHU, G. V. R. BABU, K. NAGESWARA RAO장전수학회 · Advanced Studies in Contemporary Mathematics2010 · 제20권 제4호Common Fixed Points for Weakened Compatible Mappings Satisfying the Generalized ϕ-weak Contraction Condition정찬용, DEEPAK JAIN, Sanjay Kumar한국수학교육학회 · 이론수학과 교직수학2019 · 제26권 제2호Common Fixed Points of Generalized Contractive Mappings유미자, 조선영영남수학회 · East Asian Mathematical Journal2009 · 제25권 제1호Common fixed points of weakly contractive and compatible mapsGbenga Akinbo, O.T. Mewomo장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2012 · 제15권 제4호

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