Fixed point results for almost nonexpansive mappings in $b$-metric spaces

Resumo

The aim of this paper is to introduce a new class of mappings called almost nonexpansive mappings in a $b$-metric space. Some characteristics of this class of mappings are discussed. Fixed point and common fixed point results for such mappings are obtained. An application to the Cauchy problem in a Banach space is also shown in this paper.

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Biografia do Autor

Nilakshi Goswami, Gauhati University

Assistant Professor,

Department of Mathematics

Nehjamang Haokip, Churachandpur College

Assistant Professor,

Deoartment of Mathematics,

Churachandpur College,

Manipur - 795128, India.

Referências

I. A. Bakhtin, The contraction mapping principle in almost metric spaces, Funct. Anal., Gos. Ped. Inst., Unianowsk 30, 26–37, (1989).

M. Boriceanu, Fixed point theory for multivalued generalized contraction on a set with two b-metrics, Studia Univ “Babes-Bolyai” Mathematica LIV (3), 1–14, (2009).

F. E. Browder, Nonexpansive nonlinear operators in a Banach space, Proceedings of the National Academy of Sciences of the United States of America 54 (4), 1041–1044, (1965). DOI: https://doi.org/10.1073/pnas.54.4.1041

F. E. Browder and W. V. Petryshyn, The solution by iteration of nonlinear functional equations in Banach spaces, Bull. Amer. Math. Soc. 72 (3), 571–575, (1966). DOI: https://doi.org/10.1090/S0002-9904-1966-11544-6

S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostrav. 1, 5–11, (1993).

D. Das and N. Goswami, Some fixed point theorems on the sum and product of operators in tensor product spaces, IJPAM 109, 651–663, (2016). DOI: https://doi.org/10.12732/ijpam.v109i3.13

D. Das and N. Goswami and V. N. Mishra, Some results on the projective cone normed tensor product spaces over Banach algebras, Bol. Soc. Paran. Mat. (3s.) 38 (1), 197–221, (2020). DOI: https://doi.org/10.5269/bspm.v38i1.36450

J. B. Diaz and F. T. Metcalf, On the structure of the set of subsequential limit points of successive approximations, Bulletin of the American Mathematical Society 73 (4), 516–519, (1967). DOI: https://doi.org/10.1090/S0002-9904-1967-11725-7

D. Gohde, Zum prinzip der kontraktiven abbildung, Math. Nachr. 30, 251–258, (1965). DOI: https://doi.org/10.1002/mana.19650300312

J. Gornicki, Remarks on asymptotic regularity and fixed points, J. Fixed Point Theory Appl. 21, 29, (2019). DOI: https://doi.org/10.1007/s11784-019-0668-0

N. Goswami and N. Haokip and V. N. Mishra, F-contractive type mappings in b-metric spaces and some related fixed point results, Fixed Point Theory and Applications 2019, 13, (2019). DOI: https://doi.org/10.1186/s13663-019-0663-6

N. Haokip and N. Goswami, Some fixed point theorems for generalized Kannan type mappings in b-metric spaces, Proyecciones Journal of Mathematics 38 (4), 763–782, (2019). DOI: https://doi.org/10.22199/issn.0717-6279-2019-04-0050

W. A. Kirk, A fixed point theorem for mappings which do not increase distances, American Mathematical Monthly 72 (9), 1004–1006, (1965). DOI: https://doi.org/10.2307/2313345

W. A. Kirk, Nonexpansive mappings in metric and Banach spaces, Rendiconti del Seminario Matematico e Fisico di Milano 51 (1), 133–144, (1981). DOI: https://doi.org/10.1007/BF02924816

A. Lukacs and S. Kajanto, Fixed point theorems for various types of F-contractions in complete b-metric spaces, Fixed Point Theory 19 (1), 321–334, (2018). DOI: https://doi.org/10.24193/fpt-ro.2018.1.25

S. K. Mohanta, Coincidence points and common fixed points for expansive type mappings in b-metric spaces, Iran. J. Math. Sci. Inform. 11 (1), 101–113, (2016).

R. D. Nussbaum, Degree theory for local condensing maps, Journal of Mathematical Analysis and Applications 37 (3), 741–766, (1972). DOI: https://doi.org/10.1016/0022-247X(72)90253-3

M. Ozturk and M. Basarir, On some common theorems for f-contraction mappings in cone metric spaces, Int. Journal of Math. Analysis 5 (3), 119–127, (2011

V. Pata, Fixed point theorems and applications, Springer (2019). DOI: https://doi.org/10.1007/978-3-030-19670-7

B. Patir and N. Goswami and V. N. Mishra, Some results on fixed point theory for a class of generalized nonexpansive mappings, Fixed Point Theory and Applications 2018, 19, (2018). DOI: https://doi.org/10.1186/s13663-018-0644-1

J. R. Roshan and V. Parvaneh and Z. Kadelburg, Common fixed point theorems for weakly isotone increasing mappings in ordered b-metric spaces, J. Nonlinear Sci. Appl. 7 (4), 229–245, (2014). DOI: https://doi.org/10.22436/jnsa.007.04.01

J. R. Roshan and V. Parvaneh and S. Sedghi and N. Shobkolaei and W. Shatanawi, Common fixed points of almost generalized (ψ,φ)s-contractive mappings in ordered b-metric spaces, Fixed Point Theory and Applications 2013 (1), 159, (2013). DOI: https://doi.org/10.1186/1687-1812-2013-256

B. Sims and H. Xu, Locally almost nonexpansive mappings, Communications on Applied Nonlinear Analysis 8 (3), 81–88, (2001).

B. C. Tripathy, S. Paul and N. R. Das, A fixed point theorem in a generalized fuzzy metric space, Boletim da Sociedade Paranaense de Matem´atica, 32 (2), 221–227 (2014). DOI: https://doi.org/10.5269/bspm.v32i2.20896

Publicado
2022-12-26
Seção
Artigos