Question: What Columbia University professor proved the Earle-Hamilton fixed-point theorem with Clifford Earle in 1968?

full_context: Document 1: Gelfand–Naimark theorem: In mathematics, the Gelfand–Naimark theorem states that an arbitrary C*-algebra "A" is isometrically *-isomorphic to a C*-algebra of bounded operators on a Hilbert space. This result was proven by Israel Gelfand and Mark Naimark in 1943 and was a significant point in the development of the theory of C*-algebras since it established the possibility of considering a C*-algebra as an abstract algebraic entity without reference to particular realizations as an operator algebra.
Document 2: Raúl Rabadán: Raúl Rabadán is an Associate Professor in the Department of Systems Biology and Biomedical Informatics at Columbia University. He is the director of the Center for Topology of Cancer Evolution and Heterogeneity. From 2001 to 2003, Dr. Rabadán was a fellow at the Theoretical Physics Division at CERN, the European Organization for Nuclear Research, in Geneva, Switzerland. In 2003 he joined the Physics Group of the School of Natural Sciences at the Institute for Advanced Study. During 2006-2008, Dr. Rabadán was the Martin A. and Helen Chooljian Member at The Simons Center for Systems Biology at the Institute for Advanced Study in Princeton, New Jersey. He has been named one of Popular Science's Brilliant 10 (2010), a Stewart Trust Fellow (2013), and he received the Harold and Golden Lamport Award at Columbia University (2014). At Columbia, he has put together a highly interdisciplinary lab with researchers from the fields of mathematics, physics, computer science, engineering, and medicine, with the common goal of solving pressing biomedical problems through quantitative computational models. Dr. Rabadán’s current interest focuses on uncovering patterns of evolution in biological systems—in particular, RNA viruses and cancer.
Document 3: Earle–Hamilton fixed-point theorem: In mathematics, the Earle–Hamilton fixed point theorem is a result in geometric function theory giving sufficient conditions for a holomorphic mapping of an open domain in a complex Banach space into itself to have a fixed point. The result was proved in 1968 by Clifford Earle and Richard S. Hamilton by showing that, with respect to the Carathéodory metric on the domain, the holomorphic mapping becomes a contraction mapping to which the Banach fixed-point theorem can be applied.
Document 4: Aleksandrov–Rassias problem: The theory of isometries in the framework of Banach spaces has its beginning in a paper by Stanisław Mazur and Stanisław M. Ulam in 1932. They proved that each isometry of a normed real linear space onto a normed real linear space is a linear mapping up to translation. In 1970, Aleksandr Danilovich Aleksandrov asked whether the existence of a single conservative distance for some mapping implies that it is an isometry. Themistocles M. Rassias posed the following problem:
Document 5: Richard von Mises: Richard Edler von Mises ( ; ] ; 19 April 1883 – 14 July 1953) was a scientist and mathematician who worked on solid mechanics, fluid mechanics, aerodynamics, aeronautics, statistics and probability theory. He held the position of Gordon-McKay Professor of Aerodynamics and Applied Mathematics at Harvard University. He described his work in his own words shortly before his death as being on
Document 6: Shing-Tung Yau: Shing-Tung Yau ( ; ; born April 4, 1949) is a Hong Kong and naturalised American mathematician. He was awarded the Fields Medal in 1982. He is currently the William Caspar Graustein Professor of Mathematics at Harvard.
Document 7: Qiang Du: Qiang Du, (Chinese: 杜强), Fu Foundation Professor of Applied Mathematics at Columbia University, is a mathematician and computational scientist. Prior to moving to Columbia, he was the Verne M. Willaman Professor of Mathematics at Pennsylvania State University affiliated with the Pennsylvania State University Department of Mathematics and Materials Sciences. Du was elected a fellow of SIAM on March 29, 2013 for "contributions to applied and computational mathematics with applications in material science, computational geometry, and biology."
Document 8: Nicolai Reshetikhin: Nicolai Yuryevich Reshetikhin (Russian: Николай Юрьевич Решетихин , born October 10, 1958 in Leningrad, Soviet Union) is a mathematical physicist, currently a professor of mathematics at the University of California, Berkeley and a professor of mathematical physics at the University of Amsterdam. His research is in the fields of low-dimensional topology, representation theory, and quantum groups. His major contributions are in the theory of quantum integrable systems, in representation theory of quantum groups
Document 9: Caristi fixed-point theorem: In mathematics, the Caristi fixed-point theorem (also known as the Caristi–Kirk fixed-point theorem) generalizes the Banach fixed point theorem for maps of a complete metric space into itself. Caristi's fixed-point theorem is a variation of the "ε"-variational principle of Ekeland (1974, 1979). Moreover, the conclusion of Caristi's theorem is equivalent to metric completeness, as proved by Weston (1977). The original result is due to the mathematicians James Caristi and William Arthur Kirk.
Document 10: Egorov's theorem: In measure theory, an area of mathematics, Egorov's theorem establishes a condition for the uniform convergence of a pointwise convergent sequence of measurable functions. It is also named Severini–Egoroff theorem or Severini–Egorov theorem, after Carlo Severini, an Italian mathematician, and Dmitri Egorov, a Russian physicist and geometer, who published independent proofs respectively in 1910 and 1911.
Document 11: Raymond L. Johnson: Raymond Lewis Johnson (b.1943) is an American mathematician, currently a professor emeritus at the University of Maryland, College Park and an adjunct professor of mathematics at Rice University. He was the first African-American student at Rice University, and the first African-American mathematics professor at the University of Maryland. His research concerns non-well-posed problems and harmonic analysis.
Document 12: Borel fixed-point theorem: In mathematics, the Borel fixed-point theorem is a fixed-point theorem in algebraic geometry generalizing the Lie–Kolchin theorem. The result was proved by .
Document 13: Richard S. Hamilton: Richard Streit Hamilton (born 1943) is Davies Professor of Mathematics at Columbia University.
Document 14: Rouché's theorem: Rouché's theorem, named after Eugène Rouché, states that for any two complex-valued functions "f" and "g" holomorphic inside some region "K" with closed contour formula_1, if |"g"("z")| < |"f"("z")| on formula_1, then "f" and "f" + "g" have the same number of zeros inside "K", where each zero is counted as many times as its multiplicity. This theorem assumes that the contour formula_1 is simple, that is, without self-intersections. Rouché's theorem is an easy consequence of a stronger symmetric Rouché's theorem described below.
Document 15: Gelfand–Mazur theorem: In operator theory, the Gelfand–Mazur theorem is a theorem named after Israel Gelfand and Stanisław Mazur which states that a Banach algebra with unit over the complex numbers in which every nonzero element is invertible is isometrically isomorphic to the complex numbers, i. e., the only complex Banach algebra that is a division algebra is the complex numbers C.
ground_truth: Richard S. Hamilton