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Partial Fuzzy Metric Space and Some Fixed Point Results

Shaban Sedghi, Nabi Shobkolaei, Ishak Altun (2015)

Communications in Mathematics

In this paper, we introduce the concept of partial fuzzy metric on a nonempty set X and give the topological structure and some properties of partial fuzzy metric space. Then some fixed point results are provided.

Partially dissipative periodic processes

Jan Andres, Lech Górniewicz, Marta Lewicka (1996)

Banach Center Publications

Further extension of the Levinson transformation theory is performed for partially dissipative periodic processes via the fixed point index. Thus, for example, the periodic problem for differential inclusions can be treated by means of the multivalued Poincaré translation operator. In a certain case, the well-known Ważewski principle can also be generalized in this way, because no transversality is required on the boundary.

Periodic problems for ODEs via multivalued Poincaré operators

Lech Górniewicz (1998)

Archivum Mathematicum

We shall consider periodic problems for ordinary differential equations of the form x ' ( t ) = f ( t , x ( t ) ) , x ( 0 ) = x ( a ) , where f : [ 0 , a ] × R n R n satisfies suitable assumptions. To study the above problem we shall follow an approach based on the topological degree theory. Roughly speaking, if on some ball of R n , the topological degree of, associated to (), multivalued Poincaré operator P turns out to be different from zero, then problem () has solutions. Next by using the multivalued version of the classical Liapunov-Krasnoselskǐ guiding potential...

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