The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
권호 표지
DOI QR코드

DOI QR Code

TWO SUBRAHMANYAM TYPE OF COMMON FIXED POINT THEOREMS IN COMPLETE METRIC SPACES

  • Accepted : 2023.10.09
  • Published : 2024.02.28
Download PDF
⟨ Previous Next ⟩

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 single-valued and multi-valued mappings in complete metric spaces. Our results extend and generalize the corresponding fixed point theorems in the literature [3, 6].

Keywords

References

  1. J. Caristi: Fixed point theorems for mappings satisfying inwardness conditions. Tran. Amer. Math. Soc. 215 (1976), 241-251. https://doi.org/10.1090/s0002-9947-1976-0394329-4
  2. J. Caristi & W.A. Kirk: Geometric fixed point theory and inwardness conditions. The Geometry of Metric and Linear Spaces. Lecture Notes in Mathematics, vol 490. Springer, Berlin, Heidelberg, 1975.
  3. F. Khojasteh, M. Abbas & S. Costache: Two new types of fixed point theorems in complete metric spaces. Abst. Appl. Anal. Volume 2014, Article ID 325840. https://doi. org/10.1155/2014/325840
  4. S. Leader: Equivalent Cauchy sequences and contractive fixed points in metric spaces. Studia Mathematica 76 (1983), no. 1, 63-67. https://doi.org/10.4064/sm-76-1-63-67
  5. S.B. Nadler: Multi-valued contraction mappings. Pacific J. Math. 30 (1969), 457-488. https://doi.org/10.2140/pjm.1969.30.475
  6. B.E. Rhoades: Two new fixed point theorems. Gen. Math. Notes 27 (2015), no. 2, 123-132.
  7. P.V. Subrahmanyam: Remarks on some fixed point theorems related to Banach contraction principle. J. Math. Physical Science 8 (1974), 445-457.
  8. T. Suzuki: A new type of fixed point theorem in metric space. Nonlinear Anal. 71 (2009), 5313-5317. https://doi.org/10.1016/j.na.2009.04.017