USING LEARNING ABILITIES OF COMPUTATION IN COUNTING
By
Trang Jain¹ , Ankur Jain² and Rakhi Saxena³
¹Department of Computer Science, Motilal Nehru College, University of Delhi, Delhi, India-110021
²Department of Computer Science & Engineering, IFTM University, Moradabad Uttar Pradesh, India-244001
³Department of Computer Science, Deshbandhu College, University of Delhi, Delhi, India-110019
Email: tarangjain@mln.du.ac.in, ankur1101@gmail.com, rsaxena@db.du.ac.in
(Received: March 03, 2023; In format: March 10,2023; Revised: February 17, 2024; Accepted: February 20, 2024)
DOI: https://doi.org/10.58250/jnanabha.2024.54105
Abstract
In this paper, we introduce a new notion of local or neighborhood solutions and establish a couple of approximation results for local existence and uniqueness of the solution of an IVP of nonlinear higher order ordinary hybrid differential equations by using the Dhage monotone iteration method based on the recent hybrid fixed point theorems of Dhage (2023). An approximation result for Ulam-Hyers stability of the local solution of the considered hybrid differential equation is also established. Our main abstract results of this paper are also illustrated with a couple of numerical examples. Finally, we compare our existence and uniqueness results with those existing in the literature via other operator theoretic methods from nonlinear functional analysis. We claim that the method and the results of this paper are new to the literature.
2020 Mathematical Sciences Classification: 34A12, 34A34, 34A45, 47H10
Keywords and Phrases: Ordinary differential equation; Dhage iteration method; Approximation theorems; Local existence and uniqueness; Ulam-Hyers stability.