### Extended b-metric spaces and the related approximate fixed point results

#### Abstract

#### Keywords

#### Full Text:

PDF#### References

I. A. Bakhtin. The contraction mapping principle in almost metric spaces. Funct. Anal., 30:26–37, 1989.

S. Banach. Surles operations dans les ensembles abstract et leur application aux equation integrals. Fund. Math, 3:133–181, 1922

M. Berinde. Approximate fixed point theorems. Stud. Univ. ”Babes-bolyai”, Mathematica LI, 1:11–25, 2006.

V. Berinde. Iterative approximation of fixed points. Editura efemeride, Baia Mare, 2002.

V. Berinde. On the approximation of fixed points of weak contractive mappings. Carpathian J. Math., 19(1):7–22, 2003.

R. M. T. Bianchini. Su un problema di S. Reich riguardante la teoria dei punti fissi. Bolletino U.M.I.,, 4(5):103–106, 1972.

M. Boriceanu. Fixed point theory for multivalued generalized contraction on a set with two b-metric spaces. Studia, univ.”Babes-Bolyai”, Mathematica Libertica, 3:1–14, 2009.

F. Brouwer. The fixed point theory of multiplicative mappings in topological vector spaces. Mathematische Annalen., 177:283–301, 1908.

S. K. Chatterjea. Fixed point theorems. C.R. Acad.Bulg. Sci., 25:727–730, 1972.

L. B. Ciric. Generalized contractions and fixed point theorems. Publ. Inst. Math. (Bulgr), 12(26):19–26, 1971.

B. K. Dass and S. Gupta. An extension of Banach contraction principle through rational expression. Communicated by F. C. Auluck, FNA, 1975.

P. Debnath, N. Konwar, and S. Radenovic. Metric fixed point theory, applications in Science, Engineering and Behavioural Sciences. Forum for inter disciplinary mathematics, Springer, 2021.

D. Dey and M. Saha. Approximate fixed point of Reich operator. Acta Mathematica Universitatis Comenianae, 2012.

G. E. Hardy and T. D. Rogers. A generalization of fixed point theorems of Reich. Can. Math. Bull., 16:201–206, 1973.

D. S. Jaggi. Some unique fixed point theorems. Indian Journal of Pure and Applied Mathematics, 8:223–230, 1977.

R. Kannan. Some results on fixed points. Bull Calcutta Math. Soc.,, 60:71–76, 1968.

R. Kannan. Some results on fixed points II. Am. Math. Mon., 76:405–408, 1969

E. Karapinar. A new non-unique fixed point theorem. Ann. Funct. Annals, 2(1):51–58, 2011.

M. S. Khan. A fixed point theorems for metric spaces. Rendiconti Dell ’istituto di mathematica dell’ Universtia di tresti,, 8:69–72, 1976.

S. A. Khuri and I. Louhichi. A novel Ishikawa-Green’s fixed point scheme for the solution of BVPs. Appl. Math. Lett.,, 82:50–57, 2018.

M. Marudai and V. S. Bright. Unique fixed point theorem on weakly B-contractive mappings. Far East journal of Mathematical Sciences (FJMS), 98(7):897–914, 2015.

Z. D. Mitrovic and S. Radenovi ´ c. The Banach and Reich contractions in ´ bv(s)-metric spaces. J. Fixed Point Theory Appl., 19:3087–3095, 2017.

S. A. M. Mohsenalhosseini and M. Saheli. Some of family of contractive type maps and Approximate common fixed point. J.Fixed Point Theory, (2021:2), 2021.

S. A. M. Mohsenalhosseini, H. Mzaheri, and M. A. Dehghan. Approximate best proximity pairs in metric space. Abstr. Appl. Anal., (596971), 2011.

S. A. M. Mohsenialhosseini. Approximate fixed point theorems of cyclical contraction mapping. Mathematica Moravica,, 21(1):125–137, 2017.

S. Reich. Some remarks connecting contraction mappings. Can. Math. Bull., 14: 121–124, 1971.

J. R. Roshan, V. Parvanesh, Z. Kadelburg, and N. Hussain. New fixed point results in b-rectangular metric spaces. Nonlinear Analalysis: Modelling and control, 21(5):614–634, 2016.

K. Tijani and S. Olayemi. Approximate fixed point results for rational-type contraction mappings. International Journal of Analysis and Optimization: Theory and Applications,, pages 76–86, 2021.

S. Tis, A. Torre, and R. Branzei. Approximate fixed point theorems. Libertas Mathematica, 23:35–39, 2003.

T. Zamfirescu. Fixed point theorems in metric spaces. Arch. Math.(Basel), 23: 292–298, 1972

DOI: http://dx.doi.org/10.23755/rm.v49i0.1431

### Refbacks

- There are currently no refbacks.

Copyright (c) 2023 Theivaraman R, Srinivasan P. S

This work is licensed under a Creative Commons Attribution 4.0 International License.

Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.