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

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