Enriched P-Contractions on Normed Space and a Fixed Point Result-Reference-Cited by-同舟云学术

Enriched P-Contractions on Normed Space and a Fixed Point Result

Published:2024-06-30 Issue:1 Volume:16 Page:64-69
ISSN:2148-1830
Container-title:Turkish Journal of Mathematics and Computer Science
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Author:

Altun İshak¹^ORCID,Aslan Hançer Hatice¹^ORCID,Ateş Merve Doğan¹^ORCID

Affiliation:

1. KIRIKKALE UNIVERSITY

Abstract

This paper introduces the concept of enriched $P$-contractions on linear normed spaces, and provides illustrative examples that highlight the differences between this new concept and its previous counterparts. It then gives a research result regarding the existence and uniqueness of the fixed point of this innovative type of contractions in Banach spaces. Finally, reminds us of the concept of enriched nonexpansive mappings and also offers a simple fixed point theorem for such mappings.

Publisher

Turkish Journal of Mathematics and Computer Science, Association of Mathematicians

Reference15 articles.

1. Abbas, M., Anjum, R., Ismail, N., Approximation of fixed points of enriched asymptotically nonexpansive mappings in CAT(0) spaces, Rend. Circ. Mat. Palermo, II. Ser, 72(2023), 2409–2427.

2. Banach, S., Sur les op´erations dans les ensembles abstraits et leur application aux ´equations int´egrales, Fund. Math., 3(1922), 133–181.

3. Berinde, V., Approximating fixed points of enriched nonexpansive mappings by Krasnoselskij iteration in Hilbert spaces, Carpathian J. Math., 35(2019), 293–304.

4. Berinde, V., P˘acurar, M., Approximating fixed points of enriched contractions in Banach spaces, J. Fixed Point Theory Appl., 22(2)(2020).

5. Berinde, V., P˘acurar, M., Kannan’s fixed point approximation for solving split feasibility and variational inequality problems, J. Comput. Appl. Math., 386(2021).