RESTRICTED r-BELL NUMBERS, POLYNOMIALS and (r; β)-BELL POLYNOMIALS
By
M. A. Pathan1,2 and Hemant Kumar3
1Centre for Mathematical and Statistical Sciences, Peechi Campus, Peechi, Kerala, India-680653
2Department of Mathematics, Aligarh Muslim University, Aligarh, India-202002
3Department of Mathematics, D. A-V. Postgraduate College, Kanpur, Uttar Pradesh, India-208001
Email: mapathan@gmail.com, palhemant2007@rediffmail.com
(Received: September 10, 2024; In format: October 15, 2024; Revised: November 20, 2024; Accepted: December 26, 2024)
DOI: https://doi.org/10.58250/jnanabha.2024.54232
Abstract
We prove the existence of maximal and minimal integrable solutions of nonlinear Urysohn type integral equations. Two basic integral inequalities are obtained in the form of extremal integrable solutions which are further exploited for proving the boundedness and uniqueness of the integrable solutions of the considered integral equation.
2020 Mathematical Sciences Classification: Primary 45G10 Secondary 47H10
Keywords: Urysohn integral equation; Tarski fixed point principle; Extremal integrable solutions; integral inequalities.