A Fixed-Point Problem with Mixed-Type Contractive Condition

Calogero Vetro

doi:10.33205/cma.684638

Research Article

Year 2020, Volume: 3 Issue: 1, 45 - 52, 01.03.2020

Calogero Vetro

https://doi.org/10.33205/cma.684638

Cited By: 7

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, Volume: 3 Issue: 1, 45 - 52, 01.03.2020

Calogero Vetro

https://doi.org/10.33205/cma.684638

Cited By: 7

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.

Keywords

fixed point

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 Volume: 3 Issue: 1

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.