Unique common fixed point results in C*-algebra valued metric spaces using (Φ-C∗)-contractions of hardy-rogers type

Document Type : Research Paper

Authors

1 Raiganj University, India

2 Department of Mathematics, Raiganj University , P.O. 733134, Raiganj,West Bengal, India

Abstract

In this paper we have developed C -class function and introduced (Φ-C)-contractions of Hardy-Rogers type on
C-algebra valued metric spaces.We have also established some unique common fixed point results for six maps in
C-algebra valued metric spaces using this type contractions. Some basic definitions, proper-ties and lemmas are also discussed in the introduction and prelim-inaries parts. Some corollaries and examples are also given on the basis of the results. 

Keywords


[1] M. Abbas, H. Aydi and S. Radenovic, Fixed Point of T-Hardy-Rogers Contractive Mappings in Partially Ordered Partial Metric Spaces, International Journal of Mathematics and Mathemetical Sciences, 313675(2012).
[2] H.H. Alsulami, R.P. Agarwal, E. Karapinar and F. Khojasteh, A short note on C- valued contraction mappings, Journal of Inequalities and Applications,50(2016).
[3] M. Arshad, E. Ameer and A. Hussain, Hardy-Rogers-type Fixed Point Theorems for α − GF-Contractions, Archivum Mathematicum (BRNO), 51(3), (2015),129-141.
[4] S. Banach, Sur les operations dans les ensembles abstraits et leurs applications aux equations integrales, Fundam.Math., 3, (1922), 133-181.
[5] S. Chandok, D. Kumar and C. Park, C-algebra valued metric space and fixed point theorems, Proceedings Mathematical Sciences, (2018),DOI:10.1007/s12044-019-0481-0.
[6] V. Consentino and P. Vetro, Fixed point results for F-contractive mappings of Hardy-Rogers-Type, Filomat, 28 (4), (2014), 715-722.
[7] A.S. Cvetkovic, M.P. Stanic, S. Dimitrijevic and S. Simic, Common fixed point theorems for four mappings on Cone Metric Type Space, Fixed point Theory and Applications, 589725 (2011).
[8] D. Derouiche and H. Ramoul, New fixed point results for F-contractions of Hardy-Rogers type in b-metric spaces with applications, Journal of Fixed Point Theory and Applications, 22, Article No. 86(2020).
[9] A. Farajzadeh, P. Chaudchawna and A. Kaewcharoen, Fixed point theorems for (α, η, ψ, ξ)-contractive multivalued mappings on (α, η)-complete partial metric spaces, J.Nonlinear Sci.Appl., 9, (2016), 1977-1990.
[10] J.K. Jang, J.K. Yun, N.J. Bae, J.H. Kim, D.M. Lee and S.M. Kang, Common fixed point theorems of compatible mappings in metric spaces, International Jour-nal of Pure and Applied Mathematics, 84(1), (2013), 171-183.
[11] S. Jankovic, Z. Golubovic and S. Radenovic, Compatible and weakly compatible mappings in cone metric spaces, Mathematical and Computer Modelling, 52 (9-10), (2010), 1728-1738.
[12] N. Hussain, M.A. Kutbi and P. Salimi, Fixed point theory in α-complete metric spaces with applications, Abstract and Applied Analysis, 2014, DOI: 10.1155/2014/280817.
[13] D. Kumar, D. Rishi, C. Park and R.J. Lee, On fixed point in C-algebra valued metric spaces using C∗ class function, Int.J.Nonlinear Anal.Appl., 12 (2), (2021),1157-1161.[14] Z. Ma and L. Jiang, C-Algebra valued b-metric space and related fixed pointtheorems, Fixed point theory and applications, 222(2015), DOI: 10.1186/s13663-015-0471-6, 11 pages.
[15] Z. Ma, L. Jiang and H. Sun, C-algebra valued metric spaces and related fixed point theorems, Fixed point Theory and Appl., 1, Article No. 206(2014),DOI:10.1186/1687-1812-2014-206.
[16] H. Massit and M. Rossafi, Fixed point theorem for (φ − F) contraction on C-algebra valued metric spaces, Eur.J.Math.Appl., 1 , Article No. 14(2021).300 M. Paul and K. Tiwary
[17] S.N. Mishra, Common fixed points of compatible mappings in PM-spaces,Math.Japon., 36, (1991), 283-289.
[18] N. Mlaiki, M. Asim and M. Imad, C-algebra valued Partial b-Metric Spaces and Fixed Point Results with an Application,Σ Mathematics, 1381(8), (2020), 11 pages.
[19] B. Moeini, P. Kumar and H. Aydi, Zamfirescu type contractions on C-algebra valued metric spaces, Journal of Mathematical Analysis, 9 (1), (2018), 150-161.
[20] P. Parvateesam, K. Tas and U.D. Patel, Common fixed point theorems for gen-eralized (φ, ψ)-weak contraction condition in complete metric spaces, Journal of Inequalities and Applications, Article No. 13(2015), DOI 10.1186/s13660-015-0647-y.
[21] H. Piri and P. Kumam, Some fixed point theorems concerning F-contraction in complete metric spaces, Fixed Point Theory and Applications, Article number 210(2014).
[22] H. Piri, S. Rahrovi and R. Zarghami, Some fixed point theorems on general-ized symmetric metric spaces, Asian-European Journal of Mathematics, 14 (7),Article number 2150109 (2021).
[23] S. Radenovic, P. Vetro, A. Nastasi and L.T. Quan, Coupled Fixed Point The-orems in C*-Agebra-Valued b-Metric Spaces, Appl.Math.Inform. and Mech., 9(1), (2017), 81-90.
[24] D. K. Rishi, Unification of common fixed point in C-algebra valued metric spaces, Journal of Physics: Conference Series, 2267(2022)012108.
[25] M. Rossafi, H. Massit and S. Kabbaj, Fixed point theorem for (φ, MF)- contraction on C-algebra valued metric spaces, Asian J. Math. Appl., 7, (2022), 8 pages.
[26] S. Shukla, S. Radenovic and S. Pantelic, Some Fixed Point Theorems for Presic-Hardy-Rogers Type Contractions in Metric Spaces, Journal of Mathematics,2013, Article No. 295093.
[27] E.D. Shewar, S. Batul, T. Kamran and A. Ghiura, Caristi’s fixed point theorem on C-algebra valued metric spaces, Journal of Nonlinear Science and Applications, 9, (2016), 584-588.
[28] B. Singh and S. Jain, A fixed point theorem in menger space through weak com-patibility, J.Math.Anal. and Appl., 301(2), (2005), 439-448.
[29] O. Tripak, Common fixed points of G-nonexpansive mappings on Banach Spaces with a Graph, Fixed Point Theory and Applications, Article number 87(2016).
[30] F. Vetro, F-contractions of Hardy-Rogers type and application to multistage deci-sion process, Nonlinear Analysis:Modelling and Control, 21(4), (2016), 531-546.
[31] Q. Xin, L. Jiang and Z. Ma, Common fixed point theorms in C-algebra valued metric spaces, J.Nonlinear Sci.Appl., 9, (2016), 4617-4627.
[32] Z. Xue, G. Lv, A fixed point theorem for generalized (ψ, ϕ)-weak contractions in Branciari type generalized metric spaces, Fixed Point Theory and Algorithms for Sciences and Engineering, Article No. 1(2021).
[33] Q. Yang, C. Bai, Fixed point theorem for orthogonal contraction of Hardy-Rogers-type mapping on 0-complete metric spaces, AIMS Mathematics, 5(6), (2020), 5734-5742.
[34] C. W. McArthur, Convergence of monotone nets in ordered topological vector spaces, Studia Mathematica, T.XXXIV, (1970).