Fixed point results of some nonlinear maps with applications

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ﻓﻲ ﻫﺫﻩ ﺍﻟﺭﺴﺎﻟﺔ ﺃﺜﺒﺘﻨﺎ ﻨﻅﺭﻴﺎﺕ ﺠﺩﻴﺩﺓ ﺤﻭل ﺍﻟﻨﻘﻁﺔ ﺍﻟﻤﺘﻁﺎﺒﻘﺔ ﻭﺍﻟﻨﻘﻁﺔ ﺍﻷ ﺍﻟﺜﺎﺒﺘﺔ ﺍﻟﻤﺸﺘﺭﻜﺔ ﻟﻠﺭﻭﺍﺴﻡ ﺤﺎﺩﻴﺔ ﺍﻟﻘﻴﻤﺔ ﻭﺍﻟﻤﺘﻌﺩﺩﺓ ﺍﻟﻘﻴﻤﺔ )ﻤﺘﺼﻠﺔ ﻭﺍﻟﺘﻲ ﻟﻴﺴﺕ ﺒﺎﻟﻀﺭﻭﺭﺓ ( ﻭﺫﻟﻙ ﺒﺎﺴﺘﺨﺩﺍﻡ ﺸﺭﻭﻁ ﺘﻘﻠﺹ ﺃﻭ ﺸﺭﻭﻁ ﻤﻥ ﻨﻭﻉ "ﻟﻴﺒﺸﺘﺯ " ﻓﻲ ﺍﻟﻔﻀﺎﺀﺍﺕ ﺍﻟﻤﺘﺭﻴﺔ ﻭﻤﻥ ﺜﻡ ﺇﻋﻁﺎﺀ ﺘﻁﺒﻴﻘﺎﺕ ﻋﻠﻰ ﻫﺫﻩ ﺍﻟﻨﺘﺎﺌﺞ ﻓﻲ ﻨﻅﺭﻴﺔ ﺍﻟﺘﻘﺭﻴﺏ ﻭﻤﺴﺎﺌل ﺍﻟﻘﻴﻤﺔ ﺍﻟﻤﻤﻴﺯﺓ "ﺁﻴﺠﻥ . "ﺒﺎﺴﺘﻨﺒﺎ ﻜﻤﺎ ﻗﻤﻨﺎ ﻤ ﻁ ﺨ ﻋ ﻁﻁ ﺘﻜﺭﺍﺭﻱ ﻋﺎﻡ ﻷﻱ ﺍﻟﻼ ﺎﺌﻠﺔ ﻤﻨﺘﻬﻴﺔ ﻤﻥ ﺍﻟﺭﻭﺍﺴﻡ ﺸﺒﻪ ﻤﺘﻤﺩﺩﺓ ﺍﻟﺘﻘﺎﺭﺒﻴﺔ ﻓﻲ ﻓﻀ ﺎﺀﺍﺕ"ﺒﺎﻨﺎﺥ"ﻫﺫﺍ ﺜﻡ ﺩﺭﺴﻨﺎ ﺘﻘﺎﺭﺏ ، ﺍﻟﻤﺨﻁﻁ ﺍﻟﺘﻜﺭﺍﺭﻱ ﺇﻟﻰ ﻨﻘﻁﺔ ﺜﺎﺒﺘﺔ ﻤﺸﺘﺭﻜﺔ ﻟﻬﺫﻩ ﺍﻟﻌﺎﺌﻠﺔ ﻤﻥ ﺍﻟﺭﻭﺍﺴﻡ .ﺍﻟﻌ ﺃﻴﻀﹰﺎ ﻗﺩﻤﻨﺎ ﻨﺘﺎﺌﺞ ﻤﻨﺎﻅﺭﺓ ﻟﻠﻨﺘﺎﺌﺞ ﺍﻟﺘﻲ ﺤﺼﻠﻨﺎ ﻋﻠﻴﻬﺎ ﻭﺫﻟﻙ ﻓﻲ ﺍﻟﺤﺎﻟﺔ ﺸﻭﺍﺌﻴﺔ . ﻜﻤﺎ ﺃﺜﺒﺘﻨﺎ ﻭﺠﻭﺩ ﻨﻘﻁﺔ ﺜﺎﺒﺘﺔ ﻋﺸﻭﺍﺌﻴﺔ ﻟﻠﺭﻭﺍﺴﻡ ﺍﻟﻌﺸﻭﺍﺌﻴﺔ ﺍﻟﺩﺍﺨﻠﻴﺔ ﻤﺘﻌﺩﺩﺓ ﺍﻟﻘﻴﻤﺔ ﻓﻲ ﻓﻀﺎﺀﺍﺕ "ﺒﺎﻨﺎﺥ "ﻟﻠﻔﺼل ﺍﻟﻘﺎﺒﻠﺔ ﻭﺍﻟﺘﻲ ﻟﻬﺎ ﻤﻤﻴﺯ ﻋﺩﻡ ﺇﻨﺩﻤﺎﺝ ﻭﺘﺤﺩﺏ ﺍﻟﻭﺍﺤﺩ ﺃﻗل ﻤﻥ .

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