Common fixed points of self-maps over the generalized cone b-metric spaces

Authors

  • Mallikarjun Reddy Pagidi Department of Technical Education, Government of Telangana, Government Polytechnic for Women (Minorities), Badangpet, R.R. District, Hyderabad, Telangana, India-500112

DOI:

https://doi.org/10.23755/rm.v48i0.1248

Keywords:

cone, fixed points, normal condition of a cone, generalized ƀ-cone metric space.

Abstract

The main aim of this research paper is to establish the most generalized common fixed-point theorem for two self-maps that are commuting to each other under \mathbf{T}-Kannan type contractive condition over a generalized cone \mathbb{b}-metric spaces. The novelty of this research paper is to find a common fixed point of two weekly compatible self-maps over a generalized cone \mathbb{b}-metric spaces without assuming the normality condition of a cone. We illustrate our main result with a suitable example.

References

A. Azam, M. Arshad and I. Beg, Banach contraction principle on cone rectangular metric spaces, Applicable Analysis and Discrete Mathematics, 3, 236–241.2009.

S. Banach, Sur les op´erations dans les ensembles abstraits et leur application aux´ equations int´egrales. Fundamenta Mathematicae, 3(1), 133–181, 1922.

IA. Bakhtin, The contraction mapping principle in almost metric spaces. Functional Analysis, Gos. Ped. Inst. Unianowsk, 30, 26-37, 1989.

A. Branciari, A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publicationes Mathematicae Debrecen, 57(1-2), 31-37 2000.

Chuanzhi Bai. Common fixed point theorems for generalized ordered contractive mappings on cone b-metric spaces over Banach algebras. J. Nonlinear Sci. Appl., 9, 5766–5771, 2016.

M. Frechet, Sur quelques points du calcul fonctionnel, Rendiconti Circolo Mat. Palermo, 22(1), 1–72, 1906.

L.G. Huang and X. Zhang. Cone Metric Spaces and Fixed Point Theorems of Contractive mappings. J.Math. Anal. Appl., 332, 1468-1476, 2007.

HP. Huang, S. Radenovic and G. Deng. A sharp generalization on cone b-metric space over Banach algebra. J. Nonlinear Sci. and Appl., 10, 429-435, 2017.

N. Hussain, M.H. Shah. KKM mappings in cone b-metric spaces. Comput. Math. Appl., 62, 1677–1684, 2011.

M. Rangamma, P. Mallikarjun Reddy, A fixed point theorem for Reich contractions in generalized cone b-metric spaces. International Journal of Analysis, 10 (6), 271-278, 2016.

M. Rangamma, P. Mallikarjun Reddy, A common fixed point theorem for T-contractions on generalized cone b-metric spaces. Communications in Korean Mathematical Society, 32(1), 65-74, 2017.

R. George, A. Hossam Nabwey, K. P. Reshma, and R. Rajagopalan. Generalized cone b-metric spaces and contraction principles. Mathematiqki Vesnik, 67 (4), pp. 246–257, 2015.

Virath Singh1 and Pravin Singh. Fixed point theorems in a generalized cone b-metric space. Advances in Mathematics: Scientific Journal, 10 (4), 2083–2094, 2021.

Yan Han and Shaoyuan Xu. Generalized Reich–C´iric´–Rus-type and Kannan -type Contractions in cone b-metric spaces over Banach algebras. Journal of Mathematics, Article ID 7549981, 11 pages, 2021.

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Published

2023-12-30

Issue

Vol. 48 (2023)

Section

Volume 48-2023

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