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Two Subrahmanyam Type of Common Fixed Point Theorems in Complete Metric Spaces

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In this paper, we introduce new types of weakly Picard operators being available to a much wider class of maps, and prove common fixed point theorems of Subrahmanyam type for two these weakly Picard operators in the collection of singlevalued and multi-valued mappings in complete metric spaces. Our results extend and generalize the corresponding fixed point theorems in the literature [3, 6].

Abstract

In this paper, we introduce new types of weakly Picard operators being available to a much wider class of maps, and prove common fixed point theorems of Subrahmanyam type for two these weakly Picard operators in the collection of singlevalued and multi-valued mappings in complete metric spaces. Our results extend and generalize the corresponding fixed point theorems in the literature [3, 6].

참고문헌 (8)

  1. J. Caristi, "Fixed point theorems for mappings satisfying inwardness conditions", Tran. Amer. Math. Soc, 215, pp.241~251 (1976)[DOI]
  2. J. Caristi, "The Geometry of Metric and Linear Spaces" (1975), Springer
  3. F. Khojasteh, "Two new types of fixed point theorems in com-plete metric spaces", Abst. Appl. Anal, 2014, pp.325840~[DOI]
  4. S. Leader, "Equivalent Cauchy sequences and contractive fixed points in metric spaces", Studia Mathematica, 76(1), pp.63~67 (1983)[DOI]
  5. S. B. Nadler, "Multi-valued contraction mappings", Pacific J. Math, 30, pp.457~488 (1969)[DOI]
  6. B.E. Rhoades, "Two new fixed point theorems", Gen. Math. Notes, 27(2), pp.123~132 (2015)
  7. P. V. Subrahmanyam, "Remarks on some fixed point theorems related to Banach con-traction principle", J. Math. Physical Science, 8, pp.445~457 (1974)
  8. T. Suzuki, "A new type of fixed point theorem in metric space", Nonlinear Anal, 71, pp.5313~5317 (2009)[DOI]

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