Recently, Kutbi and Sintunavarat [5] introduced the notion of generalized w α -contraction mapping and proved a fixed point theorem for such a mapping in complete metric spaces via the concept of α-admissible mapping due to Mohammadi et al. [6].
The notion of admissible set is due to Platek [1966].
Nevertheless, for the purposes of ultimate load studies, it is sufficient to engage only the active plastic hinges that are needed to generate kinematically admissible collapse patterns, without due regards to the sequence of formation of active and/or inactive sets of yielding members.
In this paper, we establish new fixed point results for -contractive multi-valued mappings onα-complete metric spaces by using the idea ofα-admissible multi-valued mapping due to Mohammadi et al.[7].
In this paper, we introduce new type of multi-valued mappings so called ((alpha,theta,k -contraction multi-valpha,theta,k -contractionme new fixed point results for such mappings in α-comappingsetric spands by using the idea of α-admissible multi-valued maprove due to Mohammadi et al. [7] and furnisomeome inewresting examples to illustrate the main results in this paper.
This methodology accounts for: (i) flow defects due to maximum admissible stresses, pressure drop and melt temperature increase; (ii) post-extrusion phenomena (shrinkage upon cooling, draw-down promoted by pulling and swelling after die exit) and (iii) flow balancing.
When the deformity exceeded a certain range, no admissible solution could be obtained, partially due to the limitation of the unilateral fixator configuration and partially due to the restricted joint rotation and translation in the fixator design.
Recently, Phiangsungnoen et al. [11] extended the Azam and Beg's main results [7] by using the concept of β F -admissible pairs which is a generalization of the notion of β-admissible pairs for multi-valued mappings due to Mohammadi et al. [12].
However, due to the restriction to admissible parameter sets (compare Sect. 3.3), large values of immunogenicity ρ imply large values of tumour growth velocity α (see Fig. 3).
If M is the Hardy-Littlewood maximal operator, defined by. then M is admissible, with, and there are well-known results, due to Muckenhoupt ([11]) and Sawyer ([12]), which characterize the boundedness of M in weighted Lebesgue spaces.
