Open AccessOn discontinuity problem with an application to threshold activation function
Author(s) -
Ni̇hal Taş
Publication year - 2022
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2202579t
Subject(s) - mathematics , discontinuity (linguistics) , metric space , combinatorics , function (biology) , fixed point theorem , fixed point , continuous function (set theory) , discrete mathematics , mathematical analysis , evolutionary biology , biology
In this paper, some discontinuity results are obtained using the number MC(t,t*) defined as MC(t,t*) = max { d(t,t*), ad(t,Tt) + (1-a)d(t*,St*), (1-a)d(t,Tt) + ad(t*,St*), b/2 [d(t,St*) + d(t*,Tt)]}, at the common fixed point. Our results provide a new and distinct solution to an open problem ?What are the contractive conditions which are strong enough to generate a fixed point but which do not force the map to be continuous at fixed point?? given by Rhoades [33]. To do this, we investigate a new discontinuity theorem at the common fixed point on a complete metric space. Also an application to threshold activation function is given.