Iterative approximation of common attractive points of further generalized hybrid mappings
Our purpose in this paper is (i) to introduce the concept of further generalized hybrid mappings, (ii) to introduce the concept of common attractive points (CAP), and (iii) to write and use Picard-Mann iterative process for two mappings. We approximate common attractive points of further generalized...
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| Vydané v: | Fixed point theory and applications (Hindawi Publishing Corporation) Ročník 2018; číslo 1; s. 1 - 10 |
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| Jazyk: | English |
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Cham
Springer International Publishing
05.03.2018
SpringerOpen |
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| Abstract | Our purpose in this paper is (i) to introduce the concept of further generalized hybrid mappings, (ii) to introduce the concept of common attractive points (CAP), and (iii) to write and use Picard-Mann iterative process for two mappings. We approximate common attractive points of further generalized hybrid mappings by using iterative process due to Khan (Fixed Point Theory Appl. 2013:69,
2013
,
https://doi.org/10.1186/1687-1812-2013-69
) generalized to the case of two mappings in Hilbert spaces without closedness assumption. Our results are generalizations and improvements of several results in the literature in different ways. |
|---|---|
| AbstractList | Our purpose in this paper is (i) to introduce the concept of further generalized hybrid mappings, (ii) to introduce the concept of common attractive points (CAP), and (iii) to write and use Picard-Mann iterative process for two mappings. We approximate common attractive points of further generalized hybrid mappings by using iterative process due to Khan (Fixed Point Theory Appl. 2013:69,
2013
,
https://doi.org/10.1186/1687-1812-2013-69
) generalized to the case of two mappings in Hilbert spaces without closedness assumption. Our results are generalizations and improvements of several results in the literature in different ways. Abstract Our purpose in this paper is (i) to introduce the concept of further generalized hybrid mappings, (ii) to introduce the concept of common attractive points (CAP), and (iii) to write and use Picard-Mann iterative process for two mappings. We approximate common attractive points of further generalized hybrid mappings by using iterative process due to Khan (Fixed Point Theory Appl. 2013:69, 2013, https://doi.org/10.1186/1687-1812-2013-69) generalized to the case of two mappings in Hilbert spaces without closedness assumption. Our results are generalizations and improvements of several results in the literature in different ways. |
| ArticleNumber | 8 |
| Author | Khan, Safeer Hussain |
| Author_xml | – sequence: 1 givenname: Safeer Hussain surname: Khan fullname: Khan, Safeer Hussain email: safeerhussain5@yahoo.com, safeer@qu.edu.qa organization: Department of Mathematics, Statistics and Physics, Qatar University |
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| Cites_doi | 10.1186/1687-1812-2013-69 10.11650/twjm/1500406216 10.22436/jnsa.010.03.31 10.1186/s13663-015-0336-z 10.1007/s00013-008-2545-8 10.22436/jnsa.008.04.08 10.1023/A:1025407607560 10.1155/2013/904164 10.11650/twjm/1500406086 |
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| Keywords | Weak convergence 47H09 Further generalized hybrid mappings 47H10 Common attractive points 47H99 |
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| References_xml | – volume: 14 start-page: 209 issue: 2 year: 2013 end-page: 219 ident: CR9 article-title: Nonlinear ergodic theorems without convexity for nonexpansive semigroups in Hilbert spaces publication-title: J. Nonlinear Convex Anal. – volume: 2013 year: 2013 ident: CR1 article-title: A Picard–Mann hybrid iterative process publication-title: Fixed Point Theory Appl. doi: 10.1186/1687-1812-2013-69 – volume: 13 start-page: 745 issue: 4 year: 2012 end-page: 757 ident: CR7 article-title: Attractive point and weak convergence theorems for new generalized hybrid mappings in Hilbert spaces publication-title: J. Nonlinear Convex Anal. – volume: 2016 year: 2016 ident: CR3 article-title: Approximating fixed points of two finite families of -asymptotically quasi-nonexpansive mappings publication-title: J. Nonlinear Funct. 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| Snippet | Our purpose in this paper is (i) to introduce the concept of further generalized hybrid mappings, (ii) to introduce the concept of common attractive points... Abstract Our purpose in this paper is (i) to introduce the concept of further generalized hybrid mappings, (ii) to introduce the concept of common attractive... |
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| SubjectTerms | Analysis Applications of Mathematics Common attractive points Differential Geometry Further generalized hybrid mappings Iterative Methods and Optimization Algorithms: A Dedication to Dr. Hong-Kun Xu Mathematical and Computational Biology Mathematics Mathematics and Statistics Topology Weak convergence |
| Title | Iterative approximation of common attractive points of further generalized hybrid mappings |
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