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: 8

https://izlik.org/JA86NY52NA

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.