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Öğe On multivalued maps for φ-contractions involving orbits with application(AIMS Press, 2021) Ali, Amjad; Arshad, Muhammad; Asif, Awais; Savaş, Ekrem; Park, Choonkil; Shin, Dong YunIn [14], Proinov established the existence of fixed point theorems regarding as a generalization of the Banach contraction principle (BCP) of self mapping under an influence of gauge function (GF). In this paper, we develop some existence results on '-contraction for multivalued maps via b-Bianchini-Grandolfi gauge function (B-GGF) in class of b-metric spaces and consequently assure the existence results in the module of simulation function as well a-admissible mapping. An extensive set of nontrivial example is given to justify our claim. At the end, we give an application to prove the existence behavior for the system of integral inclusion.Öğe Some ıterative approximation results of f ıteration process in banach spaces(MDPI, 2022) Ahmad, Junaid; Ullah, Kifayat; Ahmad, Imtiaz; Arshad, Muhammad; Jarasthitikulchai, Nantapat; Sudsutad, WeerawatIn this research, we suggest some convergence results for operators having (RCSC) condition in Banach space setting under F iterative scheme. We establish weak convergence under Opials condition and also establish some important strong convergence results under some appropriate assumptions on the domain or on the mapping. We furnish a non-trivial example of mappings having (RCSC) condition and show that its F iterative scheme is more effective than the corresponding well known iterative schemes on this particular example.