Common fixed points of two multivalued nonexpansive maps in Kohlenbach hyperbolic spaces

Safeer Hussain Khan; Mujahid Abbas

doi:10.1186/1687-1812-2014-181

Common fixed points of two multivalued nonexpansive maps in Kohlenbach hyperbolic spaces

Safeer Hussain Khan, Mujahid Abbas

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

In this paper, we introduce an iteration scheme for two multivalued maps in Kohlenbach hyperbolic spaces. This extends the single-valued iteration process due to Agarwal et al. (J. Nonlinear Convex Anal. 8(1):61-79, 2007). Using this new algorithm, we approximate common fixed points of two multivalued mappings through △-convergence and strong convergence under some weaker conditions. A necessary and sufficient condition is given for strong convergence.

MSC: 47A06, 47H09, 47H10, 49M05.

Original language	English
Article number	181
Journal	Fixed Point Theory and Algorithms for Sciences and Engineering
Volume	2014
Issue number	1
DOIs	https://doi.org/10.1186/1687-1812-2014-181
Publication status	Published - 2014
Externally published	Yes

Keywords

common fixed point
hyperbolic space
multivalued nonexpansive map
strong convergence
△-convergence

ASJC Scopus subject areas

Geometry and Topology
Applied Mathematics

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10.1186/1687-1812-2014-181

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title = "Common fixed points of two multivalued nonexpansive maps in Kohlenbach hyperbolic spaces",

abstract = "In this paper, we introduce an iteration scheme for two multivalued maps in Kohlenbach hyperbolic spaces. This extends the single-valued iteration process due to Agarwal et al. (J. Nonlinear Convex Anal. 8(1):61-79, 2007). Using this new algorithm, we approximate common fixed points of two multivalued mappings through △-convergence and strong convergence under some weaker conditions. A necessary and sufficient condition is given for strong convergence.MSC: 47A06, 47H09, 47H10, 49M05.",

keywords = "common fixed point, hyperbolic space, multivalued nonexpansive map, strong convergence, △-convergence",

author = "Khan, \{Safeer Hussain\} and Mujahid Abbas",

note = "Publisher Copyright: {\textcopyright} 2014, Khan and Abbas; licensee Springer.",

year = "2014",

doi = "10.1186/1687-1812-2014-181",

language = "English",

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journal = "Fixed Point Theory and Algorithms for Sciences and Engineering",

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T1 - Common fixed points of two multivalued nonexpansive maps in Kohlenbach hyperbolic spaces

AU - Khan, Safeer Hussain

AU - Abbas, Mujahid

PY - 2014

Y1 - 2014

N2 - In this paper, we introduce an iteration scheme for two multivalued maps in Kohlenbach hyperbolic spaces. This extends the single-valued iteration process due to Agarwal et al. (J. Nonlinear Convex Anal. 8(1):61-79, 2007). Using this new algorithm, we approximate common fixed points of two multivalued mappings through △-convergence and strong convergence under some weaker conditions. A necessary and sufficient condition is given for strong convergence.MSC: 47A06, 47H09, 47H10, 49M05.

AB - In this paper, we introduce an iteration scheme for two multivalued maps in Kohlenbach hyperbolic spaces. This extends the single-valued iteration process due to Agarwal et al. (J. Nonlinear Convex Anal. 8(1):61-79, 2007). Using this new algorithm, we approximate common fixed points of two multivalued mappings through △-convergence and strong convergence under some weaker conditions. A necessary and sufficient condition is given for strong convergence.MSC: 47A06, 47H09, 47H10, 49M05.

KW - common fixed point

KW - hyperbolic space

KW - multivalued nonexpansive map

KW - strong convergence

KW - △-convergence

UR - https://www.scopus.com/pages/publications/84924026649

U2 - 10.1186/1687-1812-2014-181

DO - 10.1186/1687-1812-2014-181

M3 - Article

AN - SCOPUS:84924026649

SN - 1687-1820

VL - 2014

JO - Fixed Point Theory and Algorithms for Sciences and Engineering

JF - Fixed Point Theory and Algorithms for Sciences and Engineering

IS - 1

M1 - 181

ER -

Common fixed points of two multivalued nonexpansive maps in Kohlenbach hyperbolic spaces

Abstract

Keywords

ASJC Scopus subject areas

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