×

zbMATH — the first resource for mathematics

Some fixed point theorems concerning \(F\)-contraction in complete metric spaces. (English) Zbl 1371.54184
Summary: In this paper, we extend the result of D. Wardowski [ibid. 2012, Paper No. 94, 6 p. (2012; Zbl 1310.54074)] by applying some weaker conditions on the self map of a complete metric space and on the mapping \(F\), concerning the contractions defined by Wardowski. With these weaker conditions, we prove a fixed point result for \(F\)-Suzuki contractions which generalizes the result of Wardowski.

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
47H10 Fixed-point theorems
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Banach, B, Sur LES opérations dans LES ensembles abstraits et leur application aux équations intégrales, Fundam. Math, 3, 133-181, (1922) · JFM 48.0201.01
[2] Suzuki, T, A new type of fixed point theorem in metric spaces, Nonlinear Anal, 71, 5313-5317, (2009) · Zbl 1179.54071
[3] Suzuki, T, Generalized distance and existence theorems in complete metric spaces, J. Math. Anal. Appl, 253, 440-458, (2001) · Zbl 0983.54034
[4] Suzuki, T, Several fixed point theorems concerning \(τ\)-distance, Fixed Point Theory Appl, 2004, 195-209, (2004) · Zbl 1076.54532
[5] Tataru, D, Viscosity solutions of Hamilton-Jacobi equations with unbounded nonlinear terms, J. Math. Anal. Appl, 163, 345-392, (1992) · Zbl 0757.35034
[6] Vályi, I, A general maximality principle and a fixed point theorem in uniform space, Period. Math. Hung, 16, 127-134, (1985) · Zbl 0551.47025
[7] Włodarczyk, K; Plebaniak, R, Quasigauge spaces with generalized quasipseudodistances and periodic points of dissipative set-valued dynamic systems, No. 2011, (2011) · Zbl 1213.81161
[8] Włodarczyk, K; Plebaniak, P, Kannan-type contractions and fixed points in uniform spaces, No. 2011, (2011) · Zbl 1311.47075
[9] Włodarczyk, K; Plebaniak, R, Contractivity of leader type and fixed points in uniform spaces with generalized pseudodistances, J. Math. Anal. Appl, 387, 533-541, (2012) · Zbl 1233.54019
[10] Edelstein, M, On fixed and periodic points under contractive mappings, J. Lond. Math. Soc, 37, 74-79, (1962) · Zbl 0113.16503
[11] Wardowski, D, Fixed point theory of a new type of contractive mappings in complete metric spaces, No. 2012, (2012) · Zbl 1310.54074
[12] Secelean, NA, Iterated function systems consisting of \(F\)-contractions, No. 2013, (2013) · Zbl 1405.28012
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.