Convergence Analysis for Generalized Yosida Inclusion Problem with Applications

Mohammad Akram, Mohammad Dilshad, Aysha Khan (), Sumit Chandok and Izhar Ahmad
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Mohammad Akram: Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi Arabia
Mohammad Dilshad: Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 4279, Tabuk 71491, Saudi Arabia
Aysha Khan: Department of Mathematics, College of Arts and Science, Wadi-Ad-Dwasir, Prince Sattam Bin Abdulaziz University, Al-Kharj 11991, Saudi Arabia
Sumit Chandok: School of Mathematics, Thapar Institute of Engineering & Technology, Patiala 147004, Punjab, India
Izhar Ahmad: Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

Mathematics, 2023, vol. 11, issue 6, 1-19

Abstract: A new generalized Yosida inclusion problem, involving A -relaxed co-accretive mapping, is introduced. The resolvent and associated generalized Yosida approximation operator is construed and a few of its characteristics are discussed. The existence result is quantified in q -uniformly smooth Banach spaces. A four-step iterative scheme is proposed and its convergence analysis is discussed. Our theoretical assertions are illustrated by a numerical example. In addition, we confirm that the developed method is almost stable for contractions. Further, an equivalent generalized resolvent equation problem is established. Finally, by utilizing the Yosida inclusion problem, we investigate a resolvent equation problem and by employing our proposed method, a Volterra–Fredholm integral equation is examined.

Keywords: Yosida inclusion; iterative algorithm; almost stability; resolvent equation; Volterra–Fredholm integral equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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