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Year 2020, , 45 - 52, 01.03.2020
https://doi.org/10.33205/cma.684638

Abstract

References

  • S.Banach: Sur les op\'erations dans les ensembles abstraits et leur application aux \'equations int\'egrales}. Fund. Math. 3 (1922), 133-181.
  • M.Jleli, B.Samet and C.Vetro: Fixed point theory in partial metric spaces via $\varphi$-fixed point's concept in metric spaces, J. Inequal. Appl. 2014:426 (2014), 9 pp.
  • A. T.-M.Lau, W.Takahashi: Invariant means and fixed point properties for nonexpansive representations of topological semigroups. Topol. Methods Nonlinear Anal. 5 (1995), 39-57.
  • A. T.-M.Lau, Y.Zhang: Fixed point properties of semigroups of non-expansive mappings}. J. Funct. Anal. 254 (2008), 2534-2554.
  • A. T.-M.Lau, Y.Zhang: Fixed point properties for semigroups of nonlinear mappings and amenability. J. Funct. Anal. 263 (2012), 2949-2977.
  • D.Reem, S.Reich and A. J.Zaslavski: \emph{Two Results in Metric Fixed Point Theory. J. Fixed Point Theory Appl. 1 (2007), 149-157.
  • S.Reich, A. J.Zaslavski: \emph{A Fixed Point Theorem for Matkowski Contractions. Fixed Point Theory 8 (2007), 303-307.
  • S.Reich, A. J.Zaslavski: \emph{A Note on Rakotch contraction. FixedPoint Theory 9 (2008), 267-273.
  • I. A.Rus, A.Petru\c{s}el and G. Petru\c{s}el: \emph{Fixed Point Theory. Cluj University Press, Cluj-Napoca (2008).
  • B.Samet, C.Vetro and F.Vetro: From metric spaces to partial metric spaces. Fixed Point Theory Appl. 2013:5 (2013), 11 pp.
  • C.Vetro, F.Vetro: Metric or partial metric spaces endowed with a finite number of graphs: a tool to obtain fixed point results}. Topology Appl. 164 (2014), 125-137.
  • D.Wardowski: Fixed points of a new type of contractive mappings in complete metric spaces}. Fixed Point Theory Appl., 2012:94 (2012), 6 pp.

A Fixed-Point Problem with Mixed-Type Contractive Condition

Year 2020, , 45 - 52, 01.03.2020
https://doi.org/10.33205/cma.684638

Abstract

We consider a fixed-point problem for mappings involving a mixed-type contractive condition in the setting of metric spaces. Precisely, we establish the existence and uniqueness of fixed point using the recent notions of $F$-contraction and $(H,\varphi)$-contraction.

References

  • S.Banach: Sur les op\'erations dans les ensembles abstraits et leur application aux \'equations int\'egrales}. Fund. Math. 3 (1922), 133-181.
  • M.Jleli, B.Samet and C.Vetro: Fixed point theory in partial metric spaces via $\varphi$-fixed point's concept in metric spaces, J. Inequal. Appl. 2014:426 (2014), 9 pp.
  • A. T.-M.Lau, W.Takahashi: Invariant means and fixed point properties for nonexpansive representations of topological semigroups. Topol. Methods Nonlinear Anal. 5 (1995), 39-57.
  • A. T.-M.Lau, Y.Zhang: Fixed point properties of semigroups of non-expansive mappings}. J. Funct. Anal. 254 (2008), 2534-2554.
  • A. T.-M.Lau, Y.Zhang: Fixed point properties for semigroups of nonlinear mappings and amenability. J. Funct. Anal. 263 (2012), 2949-2977.
  • D.Reem, S.Reich and A. J.Zaslavski: \emph{Two Results in Metric Fixed Point Theory. J. Fixed Point Theory Appl. 1 (2007), 149-157.
  • S.Reich, A. J.Zaslavski: \emph{A Fixed Point Theorem for Matkowski Contractions. Fixed Point Theory 8 (2007), 303-307.
  • S.Reich, A. J.Zaslavski: \emph{A Note on Rakotch contraction. FixedPoint Theory 9 (2008), 267-273.
  • I. A.Rus, A.Petru\c{s}el and G. Petru\c{s}el: \emph{Fixed Point Theory. Cluj University Press, Cluj-Napoca (2008).
  • B.Samet, C.Vetro and F.Vetro: From metric spaces to partial metric spaces. Fixed Point Theory Appl. 2013:5 (2013), 11 pp.
  • C.Vetro, F.Vetro: Metric or partial metric spaces endowed with a finite number of graphs: a tool to obtain fixed point results}. Topology Appl. 164 (2014), 125-137.
  • D.Wardowski: Fixed points of a new type of contractive mappings in complete metric spaces}. Fixed Point Theory Appl., 2012:94 (2012), 6 pp.
There are 12 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Calogero Vetro

Publication Date March 1, 2020
Published in Issue Year 2020

Cite

APA Vetro, C. (2020). A Fixed-Point Problem with Mixed-Type Contractive Condition. Constructive Mathematical Analysis, 3(1), 45-52. https://doi.org/10.33205/cma.684638
AMA Vetro C. A Fixed-Point Problem with Mixed-Type Contractive Condition. CMA. March 2020;3(1):45-52. doi:10.33205/cma.684638
Chicago Vetro, Calogero. “A Fixed-Point Problem With Mixed-Type Contractive Condition”. Constructive Mathematical Analysis 3, no. 1 (March 2020): 45-52. https://doi.org/10.33205/cma.684638.
EndNote Vetro C (March 1, 2020) A Fixed-Point Problem with Mixed-Type Contractive Condition. Constructive Mathematical Analysis 3 1 45–52.
IEEE C. Vetro, “A Fixed-Point Problem with Mixed-Type Contractive Condition”, CMA, vol. 3, no. 1, pp. 45–52, 2020, doi: 10.33205/cma.684638.
ISNAD Vetro, Calogero. “A Fixed-Point Problem With Mixed-Type Contractive Condition”. Constructive Mathematical Analysis 3/1 (March 2020), 45-52. https://doi.org/10.33205/cma.684638.
JAMA Vetro C. A Fixed-Point Problem with Mixed-Type Contractive Condition. CMA. 2020;3:45–52.
MLA Vetro, Calogero. “A Fixed-Point Problem With Mixed-Type Contractive Condition”. Constructive Mathematical Analysis, vol. 3, no. 1, 2020, pp. 45-52, doi:10.33205/cma.684638.
Vancouver Vetro C. A Fixed-Point Problem with Mixed-Type Contractive Condition. CMA. 2020;3(1):45-52.