Fixed Point Theorems for \(\alpha\)-\(\psi\)-Contractive Mappings of Integral Type in \(C^*\)-algebra Valued~Metric Space

Neetu; Manoj Kumar

doi:10.26713/cma.v15i3.2754

Authors

Neetu Department of Mathematics, Baba Mastnath University, Rohtak 124021, Haryana, India https://orcid.org/0009-0007-6937-1095 (unauthenticated)
Manoj Kumar Department of Mathematics, Baba Mastnath University, Rohtak 124021, Haryana, India; Department of Mathematics, Maharishi Markandeshwar (Deemed to be University), Mullana 133207, Haryana, India https://orcid.org/0000-0003-4455-8690 (unauthenticated)

DOI:

https://doi.org/10.26713/cma.v15i3.2754

Keywords:

Fixed point, α-ψ contractive mappings of integral type, C∗-algebra valued metric space

Abstract

In this paper, we introduce two classes of generalized \(\alpha\)-\(\psi\)-contractive type mappings of integral type and analyze the existence of fixed point for these mapping in \(C^*\)-algebra valued metric space. Our study extends and generalizes the result of several studies in the literature.

Views: 384Downloads: 287

Downloads

Download data is not yet available.

References

S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fundamenta Mathematicae 3(1) (1922), 133 – 181, URL: https://eudml.org/doc/213289.

M. Berzig and M.-D. Rus, Fixed point theorems for α-contractive mappings of Meir-Keeler type and applications, Nonlinear Analysis: Modelling and Control 19(2) (2014), 178 – 198, DOI: 10.15388/NA.2014.2.3.

A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, International Journal of Mathematics and Mathematical Sciences 29(9) (2002), 531 – 536, DOI: 10.1155/S0161171202007524.

E. Karapınar, P. Shahi and K. Tas, Generalized α-ψ-contractive type mappings of integral type and related fixed-point theorems, Journal of Inequalities and Applications 2014 (2014), Article number: 160, DOI: 10.1186/1029-242X-2014-160 .

F. Khojasteh, Z. Goodarzi and A. Razani, Some fixed point theorems of integral type contraction in cone metric spaces, Fixed Point Theory and Applications 2010 (2010), Article number: 189684, DOI: 10.1155/2010/189684.

Z. Ma, L. Jiang and H. Sun, C∗-Algebra-valued metric spaces and related fixed point theorems, Fixed Point Theory and Applications 2014 (2014), Article number: 206, DOI: 10.1186/1687-1812-2014-206.

I. Masmali and S. Omran, Chatterjea and C´ iric´-type fixed point theorems using (α-ψ)-contraction on C∗-algebra valued metric space, Mathematics 10(9) (2022), 1615, DOI: 10.3390/math10091615.

B. Samet, C. Vetro and P. Vetro, Fixed point theorems for α-ψ-contractive type mappings, Nonlinear Analysis: Theory, Methods & Applications 75(4) (2012), 2154 – 2165, DOI: 10.1016/j.na.2011.10.014.