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Now we prove the existence of solutions for the problem (1.3) with a non-convex valued right hand side by applying a fixed point theorem for multi-valued maps due to Covitz and Nadler.
In addition, one could also argue that the ball can't be valued right away, so it can't be taxed.
Free speech is a valued right, and we're working together to create safe learning environments for everyone — not just the select few.
Because live events are loved by television executives for their social media appeal — they are less likely to be watched with DVRs than scripted shows — Mr. Seacrest's hosting skills are especially valued right now.
"In the 21st century it is technology companies and digital content providers, even more than cable news, that can make visible the fact that owning a gun in America is a more highly valued right than the right of a black person to live through a police encounter," said Malkia Cyril, the executive director of the Center for Media Justice and an activist with Black Lives Matter.
Now we prove the existence of solutions for the problem (1.1) with a nonconvex valued right hand side by applying a fixed point theorem for multivalued map due to Covitz and Nadler (Lemma 2.4).
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In the following, we give an existence result for problem (5.46) with convex valued right-hand side.
Thus, our result dealing with a non-convex valued right-hand side of (1.1) is more general.
Now we will be concerned with existence results for problem (5.1) with nonconvex valued right-hand side.
In the following, we give our first existence result for problem (5.1) with a convex valued right-hand side.
Finally, we present an existence result for the problem (4 - 6) with nonconvex valued right-hand side by using Covitz and Nadler's fixed point theorem.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com