A new iterative scheme for finding attractive points of \((\alpha,\beta)\)-generalized hybrid set-valued mappings

Volume 10, Issue 3, pp 1228--1237 http://dx.doi.org/10.22436/jnsa.010.03.31

Publication Date: March 20, 2017 Submission Date: December 26, 2016

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Authors

Lili Chen - Post Doctoral Station for Computer Science and Technology, Harbin University of Science and Technology, Harbin 150080, China. - Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, China. Lu Gao - Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, China. Yanfeng Zhao - Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, China.

Abstract

In this paper, we first introduce the notions of \((\alpha,\beta)\)-generalized hybrid set-valued mappings, strongly attractive points, attractive points and condition \(\acute{I}\). Then we construct an iterative method for finding attractive points of \((\alpha,\beta)\)-generalized hybrid set-valued mappings and obtain some convergence theorems of the proposed iterative scheme for \((\alpha,\beta)\)-generalized hybrid set-valued mappings defined on a uniformly convex Banach space by using of condition \(\acute{I}\)and demi-compact property, respectively.

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Keywords

• Generalized hybrid set-valued mapping
• strongly attractive point
• attractive point
• uniformly convex Banach space
• condition \(\acute{I}\).

MSC

•  46B20
•  46E30

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