On some contractive mappings and a new version of implicit function theorem in topological spaces

Author:

Laha Supriti1,Garai Hiranmoy2,Petruşel Adrian3,Dey Lakshmi1

Affiliation:

1. Department of Mathematics, National Institute of Technology Durgapur, India

2. Department of Science and Humanities, Siliguri Government Polytechnic, Siliguri, India

3. Department of Mathematics, Babes,-Bolyai University Cluj-Napoca, Romania and Academy of Romanian Scientists Bucharest, Romania

Abstract

Study on existence of fixed points of contraction and contractive (type) mappings in topological spaces is a challenging task. The main goal of this article is to deal with this challenging task. To achieve our goal, we define two new contractive type mappings, namely, h-A-contractive and h-A1-contractive mappings on a topological space X, where h : X ? X ? R+ is a function and A, A1 are two collections of implicit functions. Then, we obtain some fixed point results concerning such contractive type mappings. Finally, as an application of one of the above mentioned fixed point results, we obtain a newer version of the implicit function theorem in topological spaces.

Publisher

National Library of Serbia

Reference15 articles.

1. I. Altun, H.A. Hancer, and D. Turkoglu, A common fixed point theorem on d-complete topological spaces, Carpathian J. Math. 24(1) (2008) 1-7.

2. C. Biasi, C. Gutierrez, and E.L. dos Santos, The implicit function theorem for continuous functions, Topol. Methods Nonlinear Anal. 32 (2008) 177-185.

3. Lj.B. Ćirić, Fixed point theorems in topological spaces. Fund. Math. 87 (1975) 1-5.

4. Lj.B. Ćirić, Coincidence and fixed points for maps on topological spaces. Topology Appl. 154(17)(2007) 3100-3106.

5. K.J. Chung, Fixed point theorems in topological spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. 29(11-12) (1982) 617-626.

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3