Maia's fixed point theorems for discontinuous mappings
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2023-11-22 11:40
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HOMORODAN, Paula. Maia's fixed point theorems for discontinuous mappings. In: Mathematics and IT: Research and Education, 1-3 iulie 2021, Chişinău. Chișinău, Republica Moldova: 2021, pp. 43-44.
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Mathematics and IT: Research and Education 2021
Conferința "Mathematics and IT: Research and Education "
Chişinău, Moldova, 1-3 iulie 2021

Maia's fixed point theorems for discontinuous mappings


Pag. 43-44

Homorodan Paula
 
Technical University of Cluj-Napoca
 
Disponibil în IBN: 30 iunie 2021


Rezumat

We establish new fixed point theorems for Maia’s fixed point theorem in the setting of a space with a distance, more precisely when both metrics are replaced with two distance. We also indicate some particular cases of our main results and present some examples to illustrate the theoretical results and show that our generalizations are effective. Theorem. Let X be a nonempty set, d and ½ are two H-distance on X and T : X ! X be a mapping. We suppose that:formulaThen the Picard iteration of the point x is convergent in (X; d). If, additionally the limit ¹x of the Picard sequence is a fixed point of T, then ¹x is the unique fixed point of T.Working in the general setting of a complete H-distance space, we obtained significant generalizations of Maia’s fixed point theorem in usual metric spaces.