id author title date pages extension mime words sentence flesch summary cache txt iajs-2705 Maibed, Zena Hussein; Thajil, Ali Qasem Zenali Iteration Method For Approximating Fixed Point of A δZA - Quasi Contractive mappings 2021 14 .pdf application/pdf 6076 265 84 βˆ’ π“ˆπ‘› )║𝑠𝑛 βˆ’ 𝓅 β•‘ + π›Ώπ“ˆπ‘›((1 βˆ’ 𝓉𝑛)║𝑑𝑛 βˆ’ 𝓅 β•‘ + π›Ώπ“ˆπ‘›π“‰π‘›β•‘π‘ π‘› βˆ’ 𝓅 β•‘)] + π’΅π’œ (𝓃𝑠𝑛, 𝓂𝑝) + π’΅π’œ (𝓃𝑑𝑛, 𝓂𝑝) ≀ 𝛿[(1 βˆ’ π“ˆπ‘› ) + π›Ώπ“ˆπ‘› 𝓉𝑛)║𝑠𝑛 βˆ’ 𝓅 β•‘ + 𝛿 π“ˆπ‘›(1 βˆ’ 𝓉𝑛)║𝑑𝑛 βˆ’ 𝓅 β•‘] = 𝛿[((1 βˆ’ π“ˆπ‘›(1 βˆ’ 𝛿𝓉𝑛))β•‘(1 βˆ’ π“Šπ‘› )𝑑𝑛 + π“Šπ‘›π’―π‘‘π‘› βˆ’ 𝓅 β•‘ +π›Ώπ“ˆπ‘›(1 βˆ’ 𝓉𝑛)║𝑑𝑛 βˆ’ 𝓅 β•‘] ≀ 𝛿[((1 βˆ’ π“ˆπ‘›(1 βˆ’ 𝛿𝓉𝑛 ))((1 βˆ’ π“Šπ‘› )║𝑑𝑛 βˆ’ 𝓅 β•‘ + π›Ώπ“Šπ‘›β•‘π‘‘π‘› βˆ’ 𝓅 β•‘) +π›Ώπ“ˆπ‘›(1 βˆ’ 𝓉𝑛)║𝑑𝑛 βˆ’ 𝓅 β•‘ + π’΅π’œ (𝓃𝑑𝑛, 𝓂𝑝)] ≀ 𝛿[((1 βˆ’ π“ˆπ‘›(1 βˆ’ 𝛿𝓉𝑛 ))((1 βˆ’ π“Šπ‘› ) + π“Šπ‘›))║𝑑𝑛 βˆ’ 𝓅 β•‘ + π›Ώπ“ˆπ‘›(1 βˆ’ 𝓉𝑛)║𝑑𝑛 βˆ’ 𝓅 β•‘] ≀ 𝛿[((1 βˆ’ π“ˆπ‘›(1 βˆ’ 𝛿𝓉𝑛))║𝑑𝑛 βˆ’ 𝓅 β•‘ + 𝛿 π“ˆπ‘›(1 βˆ’ 𝓉𝑛)║𝑑𝑛 βˆ’ 𝓅 β•‘] = 𝛿[((1 βˆ’ π“ˆπ‘›(1 βˆ’ 𝛿))║𝑑𝑛 βˆ’ 𝓅 β•‘] ≀ 𝛿((1 βˆ’ 𝓋(1 βˆ’ 𝛿))║𝑑𝑛 βˆ’ 𝓅 β•‘] ⁞ ≀ [ 𝛿((1 βˆ’ 𝓋(1 βˆ’ 𝛿))]𝑛║𝑑0 βˆ’ 𝓅 β•‘ Let 𝐷𝑛 = [ 𝛿((1 βˆ’ 𝓋(1 βˆ’ 𝛿))]𝑛║𝑑0 βˆ’ 𝓅 β•‘ Form Zenali-Iteration, we have, 𝑍𝐴𝑛 = (𝛿3 Consequently;β•‘π‘₯𝑛+1 βˆ’ π‘Ÿπ‘›+1β•‘ β†’ 0 as 𝑛 β†’ 0 Therefore, β•‘π‘Ÿπ‘› βˆ’ 𝓅║ ≀ β•‘π‘Ÿπ‘› βˆ’ π‘₯𝑛 β•‘ + β•‘π‘₯𝑛 βˆ’ 𝓅║ β†’ 0 as 𝑛 β†’ ∞. ∎ Now, we will prove that our new iteration is faster than many know iterations By using new contraction mappings. cache/iajs-2705.pdf txt/iajs-2705.txt