139 research outputs found
Quotient probabilistic normed spaces and completeness results
We introduce the concept of quotient in PN spaces and give some examples. We
prove some theorems with regard to the completeness of a quotient.Comment: 10 page
Nonlinear stability of a quadratic functional equation with complex involution
summary:Let be complex vector spaces. Recently, Park and Th.M. Rassias showed that if a mapping satisfies
\begin{eqnarray} f(x+i y)+ f(x-iy) = 2 f(x) - 2f(y) \end{eqnarray}
for all , , then the mapping satisfies for all , . Furthermore, they proved the generalized Hyers-Ulam stability of the functional equation () in complex Banach spaces. In this paper, we will adopt the idea of Park and Th. M. Rassias to prove the stability of a quadratic functional equation with complex involution via fixed point method
Some Krasnoselâskii-type fixed point theorems for MeirâKeeler-type mappings
In this paper, inspired by the idea of MeirâKeeler contractive mappings, we introduce MeirâKeeler expansive mappings, say MKE, in order to obtain Krasnoselâskii-type fixed point theorems in Banach spaces. The idea of the paper is to combine the notion of MeirâKeeler mapping and expansive Krasnoselâskii fixed point theorem. We replace the expansion condition by the weakened MKE condition in some variants of Krasnoselâskii fixed point theorems that appear in the literature, e.g., in [T. Xiang, R. Yuan, A class of expansive-type Krasnoselâskii fixed point theorems, Nonlinear Anal., Theory Methods Appl., 71(7â8):3229â3239, 2009]
Total boundedness in probabilistic normed spaces
In this paper, we study total boundedness in probabilistic normed space and we give criterion for total boundedness and D-boundedness in these spaces. Also we show that in general a totally bounded set is not D-bounded
New time-dependent solutions of viable Horndeski gravity
We generate new spherical and time-dependent solutions of viable Horndeski
gravity by disforming a solution of the Einstein equations with scalar field
source and positive cosmological constant. They describe dynamical objects
embedded in asymptotically FLRW spacetimes and contain apparent horizons and a
finite radius singularity that evolve in time in peculiar ways apparently not
encountered before in Einstein and "old" scalar-tensor gravity.Comment: 17 pages, 2 figure
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