Probabilistic Airy's type equation with third order minimum norm

Bhandari, Samir Kumar; Chandok, Sumit; Das, Radha Binod

doi:10.22075/ijnaa.2022.26888.3440

Probabilistic Airy's type equation with third order minimum norm

Document Type : Research Paper

Authors

Samir Kumar Bhandari ¹

Sumit Chandok ²

Radha Binod Das ³

¹ Department of Mathematics, Bajkul Milani Mahavidyalaya, Kismat Bajkul, Purba Medinipur-721655, West Bengal, India

² School of Mathematics, Thapar Institute of Engineering and Technology, Patiala-147004, Punjab, India

³ Barkhali High School, Barkhali, Amira, Diamond Harbour, South 24 Parganas-743368, India

10.22075/ijnaa.2022.26888.3440

Abstract

In the present paper, we establish some generalized cyclic contraction results through $p$-number of subsets by using two different types of t-norm, viz. Hadzic type t-norm and minimum t-norm in the setting of 2- probabilistic metric spaces. Our results generalize some existing fixed point theorems in 2-Menger spaces. Some illustrative examples and an application to the existence of a solution to Airy’s type differential equation are also provided.

Keywords

2-probabilistic metric space

Cauchy sequence

Convergence sequence

cyclic contraction

p-cyclic contraction