A generalized Suzuki–Berinde contraction that characterizes Banach spaces-Reference-Cited by-同舟云学术

A generalized Suzuki–Berinde contraction that characterizes Banach spaces

Published:2022-11-30 Issue:0 Volume:0 Page:
ISSN:1425-6908
Container-title:Journal of Applied Analysis
language:en
Short-container-title:

Author:

Abbas Mujahid¹,Anjum Rizwan²,Rakočević Vladimir³

Affiliation:

1. Department of Mathematics , Government College University , Katchery Road , Lahore 54000 , Pakistan ; and Department of Mathematics and Applied Mathematics, University of Pretoria, Hatfield 002, Pretoria, South Africa

2. Abdus Salam School of Mathematical Sciences , Government College University , Lahore , Pakistan

3. Department of Mathematics , Faculty of Sciences and Mathematics , University of Niš , Višegradska 33 , Niš 18000 , Serbia

Abstract

Abstract We introduce a large class of contractive mappings, called Suzuki–Berinde type contraction. We show that any Suzuki–Berinde type contraction has a fixed point and characterizes the completeness of the underlying normed space. A fixed point theorem for multivalued mappings is also obtained. These results unify, generalize and complement various known comparable results in the literature.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Theory and Mathematics,Statistics, Probability and Uncertainty,Mathematical Physics

Link

https://www.degruyter.com/document/doi/10.1515/jaa-2022-2007/pdf

Reference6 articles.

1. S. Banach, Sur les opérations dans les ensembles abstraits et leurs applications aux équations intégrales, Fund. Math. 3 (1922), 133–181.

2. I. Beg and S. M. A. Aleomraninejad, Fixed points of Suzuki type multifunctions on metric spaces, Rend. Circ. Mat. Palermo (2) 64 (2015), 203–207.

3. M. Edelstein, On fixed and periodic points under contractive mappings, J. Lond. Math. Soc. 37 (1962), 74–79.

4. M. Kikkawa and T. Suzuki, Three fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear Anal. 69 (2008), no. 9, 2942–2949.

5. T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008), 1861–1869.

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Completeness Problem via Fixed Point Theory;Complex Analysis and Operator Theory;2023-07-27