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Common Fixed Points for Weakened Compatible Mappings Satisfying the Generalized ϕ-weak Contraction Condition

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In this paper, we prove some common xed point theorems for pairs of weakened compatible mappings (subcompatible and occasionally weakly compatible mappings) satisfying a generalized ϕ-weak contraction condition involving various combinations of the metric functions. In fact, our results improve the results of Jain et al. [6]. Also we provide an example for validity of our results.

Abstract

In this paper, we prove some common xed point theorems for pairs of weakened compatible mappings (subcompatible and occasionally weakly compatible mappings) satisfying a generalized ϕ-weak contraction condition involving various combinations of the metric functions. In fact, our results improve the results of Jain et al. [6]. Also we provide an example for validity of our results.

참고문헌 (11)

  1. M. Aamri, "Some new common xed point theorems under strict contractive conditions", J. Math. Anal. Appl, 270, pp.181~188 (2002)
  2. Y.I. Alber, "Principle of weakly contractive maps in Hilbert spaces, New results in operator theory and its applications", Oper. Theory Adv. Appl., 98, pp.722~ (1997)
  3. H. Bouhadjera, "Common xed points Theorems for pairs of subcompatible maps", ~ (2011)
  4. D.W. Boyd, "On nonlinear contractions", Proc. Amer. Math. Soc, 20, pp.458~464 (1969)
  5. D. Jain, "Weak contraction condition for mappings involving cubic terms of the metric function", Int. J. Math. Appl. Math, 116, pp.1115~1126 (2017)
  6. D. Jain, "Weak contraction condition for compatible mappings involving cubic terms of the metric function", Far East J. Math. Sci, 103, pp.799~818 (2018)
  7. G. Jungck, "Commonxed points for noncontinuous nonself maps on nonmetric spaces", Far East J. Math. Sci, 4, pp.199~215 (1996)
  8. P.P. Murthy, "Weak contraction condition involving cubic terms of d(x; y) under the flxed point consideration", J. Math, 2013, pp.5~ (2013)
  9. R.P. Pant, "Common flxed points of four mappings", Bull. Calcutta Math. Soc, 90, pp.281~286 (1998)
  10. B.E. Rhoades, "Some theorems on weakly contractive maps", Nonlinear Anal, 47, pp.2683~2693 (2001)
  11. M.A. Al-Thaga, "Generalized I-nonexpansive selfmaps and invariant approximations", Acta Math. Sin, 24, pp.867~876 (2008)

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