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2. Contraction mapping - Wikipedia

   en.wikipedia.org/wiki/Contraction_mapping

   A contraction mapping has at most one fixed point. Moreover, the Banach fixed-point theorem states that every contraction mapping on a non-empty complete metric space has a unique fixed point, and that for any x in M the iterated function sequence x , f ( x ), f ( f ( x )), f ( f ( f ( x ))), ... converges to the fixed point.

3. Contraction (operator theory) - Wikipedia

   en.wikipedia.org/wiki/Contraction_(operator_theory)

   This notion is a special case of the concept of a contraction mapping, but every bounded operator becomes a contraction after suitable scaling. The analysis of contractions provides insight into the structure of operators, or a family of operators. The theory of contractions on Hilbert space is largely due to Béla Szőkefalvi-Nagy and Ciprian ...

4. Contraction - Wikipedia

   en.wikipedia.org/wiki/Contraction

   Edge contraction or vertex contraction, graph operations used in graph theory; Tensor contraction, an operation on one or more tensors that arises from the natural pairing of a finite-dimensional vector space and its dual; Left contraction and right contraction of multivectors in a geometric algebra, extensions of the inner product

5. Banach fixed-point theorem - Wikipedia

   en.wikipedia.org/wiki/Banach_fixed-point_theorem

   In mathematics, the Banach fixed-point theorem (also known as the contraction mapping theorem or contractive mapping theorem or Banach–Caccioppoli theorem) is an important tool in the theory of metric spaces; it guarantees the existence and uniqueness of fixed points of certain self-maps of metric spaces and provides a constructive method to find those fixed points.

6. Our Crockpot Mac & Cheese Is Impossible To Mess Up - AOL

   www.aol.com/crockpot-mac-cheese-impossible-mess...

   3/4 tsp. garlic powder. 1/8 tsp. ground nutmeg. Freshly ground black pepper. 3 c. shredded sharp cheddar. 1 c. shredded Gruyère. 1 c. shredded mozzarella. 1/3 c. sour cream, room temperature.

7. Senior Golden Retriever Spent 9 Years in a Shed as a Breeding ...

   www.aol.com/senior-golden-retriever-spent-9...

   Bruce the 9-year-old golden retriever spent most of his life living in a shed as a breeding dog for a backyard breeder . A couple adopted the senior pet in 2024 from Humane Fort Wayne