بعضي قضاياي نقطه ثابت براي نگاشت هاي انقباضي چند مقداري در فضاهاي شبه - متريك احتمالي منگر

Some fixed point theorems for contractive multivalued mappings in Menger probabilistic metric like spaces

در اﯾﻦ ﻣﻘﺎﻟﻪ اﺑﺘﺪا ﺑﺎ اﺳﺘﻔﺎده از ﺳﺎﺧﺘﺎر ﻓﻀﺎي b- ﻣﺘﺮﯾﮏ اﺣﺘﻤﺎﻟﯽ ﻣﻨﮕﺮ و ﻓﻀﺎي ﺷﺒﻪ ﻣﺘﺮﯾﮏ اﺣﺘﻤﺎﻟﯽ ﻣﻨﮕﺮ ، ﻣﻔﻬﻮم ﻓﻀﺎي ﺷﺒﻪ b- ﻣﺘﺮﯾﮏ اﺣﺘﻤﺎﻟﯽ ﻣﻨﮕﺮ را ﺗﻌﺮﯾﻒ ﻣﯽﮐﻨﯿﻢ و ﻣﺜﺎلﻫﺎﯾﯽ از اﯾﻦ ﻓﻀﺎ اراﺋﻪ ﻣﯽدﻫﯿﻢ. ﺳﭙﺲ ﺑﻌﻀﯽ ﻗﻀﺎﯾﺎي ﻧﻘﻄﻪ ﺛﺎﺑﺖ ﺑﺮاي ﻧﮕﺎﺷﺖﻫﺎي (اتا،بتا)- اﻧﻘﺒﺎﺿﯽ ﭼﻨﺪ ﻣﻘﺪاري را در اﯾﻦ ﻓﻀﺎﻫﺎ ﺑﯿﺎن و اﺛﺒﺎت ﻣﯽﻧﻤﺎﯾﯿﻢ. در اداﻣﻪ ﺑﻌﻀﯽ ﻧﺘﺎﯾﺞ از ﻧﻘﻄﻪ ﺛﺎﺑﺖ را ﺑﺮاي ﻧﮕﺎﺷﺖﻫﺎي اﻧﻘﺒﺎﺿﯽ r -بتا- ﻧﻮع ﺗﻌﻤﯿﻢ ﯾﺎﻓﺘﻪ ﺗﻌﺮﯾﻒ ﺷﺪه روي ﻓﻀﺎي ﺷﺒﻪ b- ﻣﺘﺮﯾﮏ اﺣﺘﻤﺎﻟﯽ ﻣﻨﮕﺮ ﻧﺸﺎن ﻣﯽدﻫﯿﻢ . همچنين مثال هايي جهت بررسي سودمند و كارا بودن نتايج مان ارائه مي دهيم.

In this paper, first by using the constructions of probabilistic b-metric Menger space and probabilistic metric like Menger space, we introduce probabilistic b-metric like Menger space and present some examples of it. Then, we state and prove some fixed point theorems for teta-eta contraction multivalued mappings in these spaces. We show some fixed point results for generalized gamma-beta contraction type mappings on the probabilistic b-metric like Menger space. Finally, we present an example of usefulness and applicability of our results.