Approximating fixed points of generalized α-nonexpansive mappings in Banach spaces by new faster iteration process
In this paper, we introduce a new iterative scheme to approximate fixed point of generalized α -nonexpansive mappings and then, we prove that the proposed iteration process is faster than all of Picard, Mann, Ishikawa, Noor, Agarwal, Abbas, and Thakur processes for contractive mappings. We also obta...
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| Veröffentlicht in: | Numerical algorithms 2019-07, Vol.81 (3), p.1129-1148 |
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| container_title | Numerical algorithms |
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| creator | Piri, H. Daraby, B. Rahrovi, S. Ghasemi, M. |
| description | In this paper, we introduce a new iterative scheme to approximate fixed point of generalized
α
-nonexpansive mappings and then, we prove that the proposed iteration process is faster than all of Picard, Mann, Ishikawa, Noor, Agarwal, Abbas, and Thakur processes for contractive mappings. We also obtain some weak and strong convergence theorems for generalized
α
-nonexpansive mappings. At the end, by using an example for generalized
α
-nonexpansive mappings, we compare the convergence behavior of new iterative process with other iterative processes. |
| doi_str_mv | 10.1007/s11075-018-0588-x |
| format | Article |
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α
-nonexpansive mappings and then, we prove that the proposed iteration process is faster than all of Picard, Mann, Ishikawa, Noor, Agarwal, Abbas, and Thakur processes for contractive mappings. We also obtain some weak and strong convergence theorems for generalized
α
-nonexpansive mappings. At the end, by using an example for generalized
α
-nonexpansive mappings, we compare the convergence behavior of new iterative process with other iterative processes.</description><identifier>ISSN: 1017-1398</identifier><identifier>EISSN: 1572-9265</identifier><identifier>DOI: 10.1007/s11075-018-0588-x</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Algebra ; Algorithms ; Banach spaces ; Computer Science ; Convergence ; Mathematics ; Numeric Computing ; Numerical Analysis ; Original Paper ; Theorems ; Theory of Computation</subject><ispartof>Numerical algorithms, 2019-07, Vol.81 (3), p.1129-1148</ispartof><rights>Springer Science+Business Media, LLC, part of Springer Nature 2018</rights><rights>Springer Science+Business Media, LLC, part of Springer Nature 2018.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c231x-eac44d2a264cfa994a573ae15605ed1b10163f190d29d5fc904a72a392f331613</citedby><cites>FETCH-LOGICAL-c231x-eac44d2a264cfa994a573ae15605ed1b10163f190d29d5fc904a72a392f331613</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11075-018-0588-x$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11075-018-0588-x$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Piri, H.</creatorcontrib><creatorcontrib>Daraby, B.</creatorcontrib><creatorcontrib>Rahrovi, S.</creatorcontrib><creatorcontrib>Ghasemi, M.</creatorcontrib><title>Approximating fixed points of generalized α-nonexpansive mappings in Banach spaces by new faster iteration process</title><title>Numerical algorithms</title><addtitle>Numer Algor</addtitle><description>In this paper, we introduce a new iterative scheme to approximate fixed point of generalized
α
-nonexpansive mappings and then, we prove that the proposed iteration process is faster than all of Picard, Mann, Ishikawa, Noor, Agarwal, Abbas, and Thakur processes for contractive mappings. We also obtain some weak and strong convergence theorems for generalized
α
-nonexpansive mappings. At the end, by using an example for generalized
α
-nonexpansive mappings, we compare the convergence behavior of new iterative process with other iterative processes.</description><subject>Algebra</subject><subject>Algorithms</subject><subject>Banach spaces</subject><subject>Computer Science</subject><subject>Convergence</subject><subject>Mathematics</subject><subject>Numeric Computing</subject><subject>Numerical Analysis</subject><subject>Original Paper</subject><subject>Theorems</subject><subject>Theory of Computation</subject><issn>1017-1398</issn><issn>1572-9265</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNp1kMtOAyEUhonRxFp9AHckrlEODDPDsjbekiZudE3oDFSalkGY6uhb-SI-kzRj4soNh3D-S_gQOgd6CZRWVwmAVoJQqAkVdU2GAzQBUTEiWSkO851CRYDL-hidpLSmNLtYNUFpFkLsBrfVvfMrbN1gWhw65_uEO4tXxpuoN-4zv35_Ed95MwTtk3szeKtDyJ6EncfX2uvmBaegG5Pw8gN7846tTr2J2OUjp3ce56a8TqfoyOpNMme_c4qeb2-e5vdk8Xj3MJ8tSMM4DMTopihapllZNFZLWWhRcW1AlFSYFpb5SyW3IGnLZCtsI2mhK6a5ZJZzKIFP0cWYm3tfdyb1at3tos-VikmoCwlQ0qyCUdXELqVorAox44gfCqjas1UjW5XZqj1bNWQPGz0pa_3KxL_k_00_QYx_Ng</recordid><startdate>20190701</startdate><enddate>20190701</enddate><creator>Piri, H.</creator><creator>Daraby, B.</creator><creator>Rahrovi, S.</creator><creator>Ghasemi, M.</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>L6V</scope><scope>M7S</scope><scope>P62</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope></search><sort><creationdate>20190701</creationdate><title>Approximating fixed points of generalized α-nonexpansive mappings in Banach spaces by new faster iteration process</title><author>Piri, H. ; Daraby, B. ; Rahrovi, S. ; Ghasemi, M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c231x-eac44d2a264cfa994a573ae15605ed1b10163f190d29d5fc904a72a392f331613</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Algebra</topic><topic>Algorithms</topic><topic>Banach spaces</topic><topic>Computer Science</topic><topic>Convergence</topic><topic>Mathematics</topic><topic>Numeric Computing</topic><topic>Numerical Analysis</topic><topic>Original Paper</topic><topic>Theorems</topic><topic>Theory of Computation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Piri, H.</creatorcontrib><creatorcontrib>Daraby, B.</creatorcontrib><creatorcontrib>Rahrovi, S.</creatorcontrib><creatorcontrib>Ghasemi, M.</creatorcontrib><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection><jtitle>Numerical algorithms</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Piri, H.</au><au>Daraby, B.</au><au>Rahrovi, S.</au><au>Ghasemi, M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Approximating fixed points of generalized α-nonexpansive mappings in Banach spaces by new faster iteration process</atitle><jtitle>Numerical algorithms</jtitle><stitle>Numer Algor</stitle><date>2019-07-01</date><risdate>2019</risdate><volume>81</volume><issue>3</issue><spage>1129</spage><epage>1148</epage><pages>1129-1148</pages><issn>1017-1398</issn><eissn>1572-9265</eissn><abstract>In this paper, we introduce a new iterative scheme to approximate fixed point of generalized
α
-nonexpansive mappings and then, we prove that the proposed iteration process is faster than all of Picard, Mann, Ishikawa, Noor, Agarwal, Abbas, and Thakur processes for contractive mappings. We also obtain some weak and strong convergence theorems for generalized
α
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α
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| subjects | Algebra Algorithms Banach spaces Computer Science Convergence Mathematics Numeric Computing Numerical Analysis Original Paper Theorems Theory of Computation |
| title | Approximating fixed points of generalized α-nonexpansive mappings in Banach spaces by new faster iteration process |
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