Abhishikta Das - Department of Mathematics, Siksha-Bhavana, Visva-Bharati, Santiniketan-۷۳۱۲۳۵, Birbhum, West Bengal, India
Tarapada Bag - Department of Mathematics, Siksha-Bhavana, Visva-Bharati, Santiniketan-۷۳۱۲۳۵, Birbhum, West Bengal, India

Following 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.

Parametric metric, decomposition theorem, metric, generalized parametric metric