Paper's Title:

Random Fixed Point Result in Banach Space

Author(s):

¹Anwesha Ghorai, ²Samriddhi Ghosh, ³Sneha Khandait, ⁴Aditya Ghosh, ⁵Ramakant Bhardwaj, ⁶Satyendra Narayan

¹Department of Mathematics,
Amity University, Kolkata, West Bengal,
India^.
E-mail: anweshaghorai596@gmail.com

²Department of Mathematics,
Amity University, Kolkata, West Bengal, India.
E-mail: ritha98@gmail.com

³Engineering Science and Humanities department,
Thakur College of Engineering and Technology, Mumbai, Maharashtra,
India.
E-mail: sneha.khandait@tcetmumbai.in

⁴Department of Mathematics,
Amity University, Kolkata, West Bengal,
India.
E-mail: ghosh.aditya.iitg08@gmail.com

⁵Department of Mathematics,
Amity University, Kolkata, West Bengal,
India.
E-mail: drrkbhardwaj@gmail.com

⁶School of Computer Science and Technology,
Algoma University, Brampton, Ontario,
Canada.
E-mail: narayan.satyendra@gmail.com

Abstract:

The present paper deals with an extension of classical fixed point theory using random variable for advancement because it has far-reaching applications in calculus, optimization, and stochastic processes. However, many nonlinear operators arise in applied mathematics which do not fulfill the strict contraction conditions of the classical Banach principle. This limitation has inspired the development of generalized non-contractive mappings. New generalized contractive-type conditions for random operators in a complete probability measure space as well as Banach space are established. The proposed conditions incorporate nonlinear, fractional, and minimum-type terms. Random fixed point theorem are proved for rational inequalities. These results not only generalize existing theorems, but also contribute to further development of functional analysis and its applications in mathematical modeling.

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