Geodesic
On discontinuity problem with an application to threshold activation function
Filomat, Tome 36 (2022) no. 2, p. 579

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DOI

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∗), b2 [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
DOI : 10.2298/FIL2202579T
Classification : 54H25, 47H10, 55M20
Keywords: fixed point, common fixed point, discontinuity 
Nihal Taşa. On discontinuity problem with an application to threshold activation function. Filomat, Tome 36 (2022) no. 2, p. 579 . doi: 10.2298/FIL2202579T
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     author = {Nihal Ta\c{s}a},
     title = {On discontinuity problem with an application to threshold activation function},
     journal = {Filomat},
     pages = {579 },
     year = {2022},
     volume = {36},
     number = {2},
     doi = {10.2298/FIL2202579T},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2202579T/}
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