Some fixed point results on Mb-cone metric space over Bannach algebra

Jerolina Fernandez; Santosh Kumar; Neeraj Malviya

doi:10.5269/bspm.77377

Jerolina Fernandez Department of Science, The Bhopal School of Social Sciences, Bhopal, M.P., India
Santosh Kumar University of Dar es Salaam, Tanzania
Neeraj Malviya Government College, Timarni, M.P., India

Resumo

In this paper, we introduce the notion of Mb-cone metric space over Banach algebra as a generalization of both M-cone metric space over Banach algebra and b-metric spaces. In this work, we prove Kannan’s and Chatterjea’s fixed point theorems in the framework of Mb-cone metric space over Banach algebra. Illustrative examples are presented to justify our main results.

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Biografia do Autor

Jerolina Fernandez, Department of Science, The Bhopal School of Social Sciences, Bhopal, M.P., India

Associate Professor,

Department of Science,

The Bhopal School of Social Sciences,

Bhopal, M.P., India

Neeraj Malviya, Government College, Timarni, M.P., India

Associate Professor,
Department of Mathematics,

Government College, Timarni, M.P., India

Referências

M. Asadi, E. Karapinar and P. Salimi, New extension of p-metric spaces with some fixed-point results on M-metric spaces, J. of Inequalities and Appl., 2014, 18 (2014). https://doi.org/10.1186/1029-242X-2014-18

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

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

J. Fernandez, N. Malviya and Ersin Gilic, Fixed point results in M-cone metric space over Banach algebra with an application, Filomat 36:16 (2022), 5547–5562 https://doi.org/10.2298/FIL2216547.

J. Fernandez, N. Malviya, Z. D. Mitrovic, A. Hussain, V. Parvaneh, Some fixed point results on Nb-cone metric spaces over Banach algebra, Adv. Diff. Equ., 2020:529 https://doi.org/10.1186/s13662-020-02991-5, (2020).

J. Fernandez, K. Saxena and N. Malviya, On cone b2-metric spaces over Banach algebra, Sao Paulo J. Math. Sci., 11, 221-239, (2017).

J. Fernandez, N. Malviya, D. Djekic-Dolicanin, D. Puˇcic, The pb-cone metric spaces over Banach algebra with applications, Filomat, 34(3), 983-998, (2020).

M. Frechet, Sur quelques points du calcul fonctionnel, Palermo Rend., 22, 1-74, (1906).

L. G. Huang, and X. Zhang, Cone metric spaces and fixed point theorems for contractive mappings, J. Math. Anal. Appl., 332(2), 1468-1476, (2007).

H. Huang and S. Radenovic, Common fixed point theorems of Generalized Lipschitz mappings in cone metric spaces over Banach algebras, Appl. Math. Inf. Sci. 9, No. 6, 2983-2990 (2015).

Z. Kadelburg and S. Radenovic, A note on various types of cones and fixed point results in cone metric spaces, Asian J. Math. Appl., (2013).

H. Liu, and S. Xu, Cone metric spaces with Banach algebras and fixed point theorems of generalized Lipschitz mappings, Fixed Point Theory Appl., 320 (2013).

S. Matthews, Partial metric topology, 8th Summer Conference on General topology and Appl., 183-197, (1994).

S. Radenovic, and B.E. Rhoades, Fixed point theorem for two non-self mappings in cone metric spaces, Comput. Math. Appl. 57, 1701-1707 (2009).

Sh. Rezapour, and R. Hamlbarani, Some notes on the paper, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 345, 719-724, (2008).

W. Rudin, Functional Analysis, 2nd Edn. McGraw-Hill, New York (1991).

S. Shukla, S. Rai and R. Shukla, A relation-theoretic set-valued version of Preˇsic- Ciric theorem and applications, Bound Value Probl 2023, 59 (2023).

S. Shukla, N. Dubey and R. Shukla, Fixed point theorems in graphical cone metric spaces and application to a system of initial value problems, J Inequal Appl 2023, 91 (2023).

S. Xu and S. Radenovic, Fixed point theorems of generalized Lipschitz mappings on cone metric spaces over Banach algebras without assumption of normality, Fixed Point Theory and Appl., (2014).