Iterative schemes for numerical reckoning of fixed points of new nonexpansive mappings with an application-Reference-Cited by-同舟云学术

Iterative schemes for numerical reckoning of fixed points of new nonexpansive mappings with an application

Published:2023 Issue:5 Volume:8 Page:10711-10727
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Ullah Kifayat¹,Ahmad Junaid²,Hammad Hasanen A.³⁴,George Reny⁵

Affiliation:

1. Department of Mathematical Sciences, University of Lakki Marwat, Lakki Marwat 28420, Khyber Pakhtunkhwa, Pakistan

2. Department of Mathematics and Statistics, International Islamic University, H-10, Islamabad-44000, Pakistan

3. Department of Mathematics, Unaizah College of Sciences and Arts, Qassim University, Buraydah 52571, Saudi Arabia

4. Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt

5. Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia

Abstract

<abstract><p>The goal of this manuscript is to introduce a new class of generalized nonexpansive operators, called $ (\alpha, \beta, \gamma) $-nonexpansive mappings. Furthermore, some related properties of these mappings are investigated in a general Banach space. Moreover, the proposed operators utilized in the $ K $-iterative technique estimate the fixed point and examine its behavior. Also, two examples are provided to support our main results. The numerical results clearly show that the $ K $-iterative approach converges more quickly when used with this new class of operators. Ultimately, we used the $ K $-type iterative method to solve a variational inequality problem on a Hilbert space.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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