Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682214120230101A generalization to parametric metric spaces229244683510.22075/ijnaa.2022.26832.3420ENAbhishikta DasDepartment of Mathematics, Siksha-Bhavana, Visva-Bharati, Santiniketan-731235, Birbhum, West Bengal, India0000-0002-2860-424XTarapada BagDepartment of Mathematics, Siksha-Bhavana, Visva-Bharati, Santiniketan-731235, Birbhum, West Bengal, India0000-0002-8834-7097Journal Article20220411Following the concept of parametric metric space introduced by N. Hussain et al., the definition of generalized parametric metric space is given. A decomposition theorem from a generalized metric into a family of crisp metrics is established. Another decomposition theorem from a family of the crisp metric into a generalized parametric metric identical to the first one under certain conditions is proved. Some basic results are studied and develop a Banach type fixed point theorem with an application to an integral equation.https://ijnaa.semnan.ac.ir/article_6835_4735dc9b2dcd5e0e906bbd1528e95e02.pdf