Common Fixed Point Theorems For (ϕ,F)- Integral Type Contractive Mapping On C^*-algebra Valued b-metrix Space

K Maheshwaran, R . Jahir Hussain


The object of this paper, we establish the concept of integral type of common fixed point theorem for new type of generalized -valued contractive mapping. The main theorem is an existence and uniqueness of common fixed-point theorems for self-mappings with -contractive conditions on complete -algebra valued -metric space. Moreover, some illustrated examples are also provided.


C^*-algebra valued, b-metric spaces, integral type contraction, common fixed point.

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H. Alsulami, R. Agarwal, E. Karapınar, and F. Khojasteh, "Short note on c∗-valued contraction mappings," Journal of Inequalities and Application, vol. 2016, no. 50, pp. 1-3, 2016.

A. Branciari, "A fixed point theorem for mappings satisfying a general contractive condition of integral type," International Journal of Mathematics and Mathematical Sciences, vol. 29, pp. 531-536, 2002.

T. Kamran, M. Postolache, A. Ghiura, S. Batul, and R. Ali, "The Banach contraction principle in c∗-algebra-valued b-metric spaces with application," Fixed Point Theory and Applications, vol. 2016, no. 10, pp. 1-7, 2016.

Z. Liu, H. Wu, J. Ume, and S. Kang, "Some fixed point theorems for mappings satisfying contractive conditions of integral type," Fixed Point Theory and Applications, vol. 2014, no. 69, pp. 1-14, 2014.

Z. Liu, M. He, X. Liu, and L. Zhao, "Common fixed point theorems for four mappings satisfying contractive inequalities of integral type," Nonlinear Functional Analysis and Applications, vol. 23, pp. 473-501, 2018.

Z. Ma and L. Jiang, "c∗-algebra-valued b-metric spaces and related fixed point theorems," Fixed Point Theory and Applications, vol. 2015, no. 1, pp. 1-12, 2015.

Z. Ma, L. Jiang, and H. Sun, "c∗-algebra-valued metric spaces and related fixed point theorems," Fixed Point Theory and Applications, vol. 2014, no. 206, pp. 1-11, 2014.

R. Mustafa, S. Omran, and Q. Nguyen, "Fixed point theory using ψ contractive mapping in c∗−algebra valued b-metric space," Mathematics, vol. 9, no. 92, pp. 1-8, 2021.



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