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Associate Professor Brailey Sims

Conjoint Associate Professor

School of Mathematical and Physical Sciences (Mathematics)

Career Summary

Biography

Research Expertise
Sims' broad area of research is functional and nonlinear analysis, in which he has published over 60 refereed research papers in major international journals. More specifically his interest and expertise is in geometry in both Banach spaces and convex metric spaces, attainment problems and the use of embedding techniques (for example, embedding into ultrapowers) for solving such problems. His investigations have included attainment problems associated with boundary points of operator numerical ranges, and more recently the attainment of fixed points by various classes of mappings. Nonlinear optimization and control leads to variational inequalities and hence to fixed points. Equilibria of dynamical systems correspond to fixed points, whose approximability relate to the stability and ergodic behaviour of the system. The research aims to further our understanding of nonexpansive type mappings, with an emphasis on establishing easily verified, yet widely applicable, criteria for the existence of a fixed together with effective iterative algorithms for their approximation. Of particular interest are the little understood cases where the underlying space admits no natural linear structure or nice geometry, so the usual tools of convex analysis are inapplicable. Geodesic metric spaces and notions of hyperbolicity are a fertile setting for investigations while ultraproduct methods provide powerful techniques.

Teaching Expertise
Sims has taught undergraduate courses in most areas of pure mathematics, and some in applied mathematics; in particular mathematical modelling in the life sciences, operations research and optimization. These have been at all levels; pre-undergraduate to honours and to students of all ability levels.

Administrative Expertise
Head of Department/School Deputy President of Academic Senate Member of numerous selection and diverse other University Committies.

Qualifications

  • PhD, University of Newcastle
  • Bachelor of Science, University of Newcastle
  • Bachelor of Science (Honours), University of Newcastle

Keywords

  • All areas at undergraduate level
  • At all levels
  • Banach space geometry
  • Functional Analysis
  • Functional analysis at graduate level
  • Metric fixed point theory
  • Nonlinear Analysis
  • Ultraproducts of metric and Banach space

Fields of Research

Code Description Percentage
010299 Applied Mathematics not elsewhere classified 35
010199 Pure Mathematics not elsewhere classified 65

Professional Experience

Academic appointment

Dates Title Organisation / Department
1/01/1995 -  Membership - Australian mathematical society Australian mathematical society
Australia
1/03/1972 - 1/12/1989 Lecturer/Senior Lecturer University of New England
Department of Mathematics

Membership

Dates Title Organisation / Department
Assistant Editor Journal of Fixed Point Theory and Applications
Australia
Associate Editor - Jourenal of Nonlinear Analysis - Theory, Methods and Applications Jourenal of Nonlinear Analysis - Theory, Methods and Applications
Australia
Assistant Editor - Journal of Mathematical Analysis and Applications Journal of Mathematical Analysis and Applications
Australia

Invitations

Participant

Year Title / Rationale
2005 7th International Conference on Fixed point Theory and Applications
Organisation: CIMAT Description: Member of Scientific Committee Member of Organizing Committee Editor of Proceedings Keynote speaker
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Publications

For publications that are currently unpublished or in-press, details are shown in italics.


Book (1 outputs)

Year Citation Altmetrics Link
2001 Kirk WA, Sims B, Handbook of Metric Fixed Point Theory, Kluwer Academic Publishers, Dortrecht/Boston/London, 702 (2001) [A3]

Chapter (6 outputs)

Year Citation Altmetrics Link
2013 Kozlowski WM, Sims B, 'On the Convergence of Iteration Processes for Semigroups of Nonlinear Mappings in Banach Spaces', Computational and Analytical Mathematics, Springer, New York 463-484 (2013) [B1]
DOI 10.1007/978-1-4614-7621-4_22
Citations Scopus - 1
2011 Borwein JM, Sims B, 'The Douglas-Rachford algorithm in the absence of convexity', Fixed-Point Algorithms for Inverse Problems in Science and Engineering, Springer, New York 93-109 (2011) [B1]
DOI 10.1007/978-1-4419-9569-8_6
Citations Scopus - 1Web of Science - 15
2001 Sims AD, Sims B, 'Assessing the minimality of change in belief revision: capacities', Frontiers in Belief Revision, Kluwer Academic Publishers, Dortrecht/Boston/London 163-177 (2001) [B1]
2001 Sims B, 'Examples of fixed point free mappings', Handbook of Metric Fixed Point Theory, Kluwer Academic Publishers, Dortrecht/Boston/London 35-48 (2001) [B1]
2001 Khamsi MA, Sims B, 'Ultra-methods in fixed point theory', Handbook of Metric Fixed Point Theory, Kluwer Academic Publishers, Dortrecht/Boston/London 177-199 (2001) [B1]
2001 Chen S, Cui Y, Hudzik H, Sims B, 'Geometric properties related to fixed point theory in some Banach function lattices', Handbook of Metric Fixed Point Theory, Kluwer Academic Publishers, Dortrecht/Boston/London 339-389 (2001) [B1]
Show 3 more chapters

Journal article (42 outputs)

Year Citation Altmetrics Link
2016 Sims B, Bendit T, 'The structure of the norned lattice generated by the closed bounded convex subsets of a norned space', Journal of Nonlinear and Convex Analysis, 17 1069-1081 (2016)
2015 Borwein JM, Sims B, Tam MK, 'Norm convergence of realistic projection and reflection methods', Optimization, 64 161-178 (2015) [C1]

© 2014 Taylor & Francis.We provide sufficient conditions for norm convergence of various projection and reflection methods, as well as giving limiting examples regarding converge... [more]

© 2014 Taylor & Francis.We provide sufficient conditions for norm convergence of various projection and reflection methods, as well as giving limiting examples regarding convergence rates.

DOI 10.1080/02331934.2014.947499
2014 Borwein D, Borwein JM, Sims B, 'On the Solution of Linear Mean Recurrences', AMERICAN MATHEMATICAL MONTHLY, 121 486-498 (2014) [C1]
DOI 10.4169/amer.math.monthly.121.06.486
Citations Scopus - 2Web of Science - 3
2012 Bacak M, Searston IJ, Sims B, 'Alternating projections in CAT(0) spaces', Journal of Mathematical Analysis and Applications, 385 599-607 (2012) [C1]
Citations Scopus - 15Web of Science - 15
2012 Cui Y, Hudzik H, Sims B, 'Properties (UÃ2)* and (WÃ2) in Orlicz spaces and some of their consequences', Journal of Mathematical Analysis and Applications, 387 400-409 (2012) [C1]
2011 Khandani H, Vaezpour SM, Sims B, 'Common fixed points of generalized multivalued contraction on complete metric spaces', Journal of Computational Analysis and Applications, 13 1025-1038 (2011) [C1]
Citations Scopus - 5Web of Science - 5
2010 Goebel K, Sims B, 'Mean Lipschitzian mappings', Contemporary Mathematics, 513 157-167 (2010) [C1]
DOI 10.1090/conm/513
Citations Web of Science - 3
2009 Mustafa Z, Sims B, 'Fixed point theorems for contractive mappings in complete G-metric spaces', Fixed Point Theory and Applications, 9 1-10 (2009) [C1]
DOI 10.1155/2009/917175
Citations Scopus - 161Web of Science - 123
2006 Dhompongsa S, Kirk WA, Sims B, 'Fixed points of uniformly lipschitzian mappings', Nonlinear Analysis-Theory Methods & Applications, 65 762-772 (2006) [C1]
DOI 10.1016/j.na.2005.09.044
Citations Scopus - 117Web of Science - 97
2006 Mustafa ZY, Sims B, 'A new approach to generalized metric spaces', Journal of Nonlinear and Convex Analysis, 7 289-297 (2006) [C1]
Citations Web of Science - 207
2005 Kirk WA, Sims B, 'An ultrafilter approach to locally almost nonexpansive maps', Nonlinear Analysis, Theory, Methods and Applications, 63 e1241-e1251 (2005) [C1]
DOI 10.1016/j.na.2004.10.017
Citations Scopus - 3Web of Science - 4
2003 Dominguez T, Hudzik H, Lopez G, Mastylo M, Sims B, 'Complete characterizations of Kadec-Klee properties in Orlicz spaces', HOUSTON JOURNAL OF MATHEMATICS, 29 1027-1044 (2003)
Citations Scopus - 19Web of Science - 16
2003 Tomas D, Genaro L, Henryk H, Mastylo M, Sims B, 'Complete characterization of Kadec-Klee properties in Orlicz spaces', Houston Journal of Mathematics, 29 1027-1044 (2003) [C1]
2002 Li G, Sims B, 'Fixed point theorems for mappings of asymptotically nonexpansive type', Nonlinear Analysis, 50 1085-1091 (2002) [C1]
Citations Scopus - 5Web of Science - 5
2001 Sims B, Xu H-K, 'Locally almost nonexpansive mappings', Communications on Applied Nonlinear Analysis, 8 81-88 (2001) [C1]
2001 Kirk WA, Sims B, 'Uniform normal structure and related notions', Journal of Nonlinear and Convex Analysis, 2 129-138 (2001) [C1]
2000 Kirk WA, Sims B, Yuan GX-Z, 'The Knaster-Kuratowski and Mazurkiewicz theory in hyperconvex metric spaces and some of its applications', Nonlinear Analysis, 39 611-627 (2000) [C1]
Citations Scopus - 41Web of Science - 32
2000 Park S, Sims B, 'Remarks on fixed point theorems in hyperconvex spaces', Nonlinear Funct. Anal. & Appl., 5 51-64 (2000) [C1]
1999 Sims B, Smyth MA, 'On some Banach space properties sufficient for weak normal structure and their permanence properties', TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 351 497-513 (1999)
DOI 10.1090/S0002-9947-99-01862-0
Citations Scopus - 19Web of Science - 17
1999 Kirk WA, Sims B, 'Convergence of Picard Iterates of Nonexpansive Mappings', Bulletin of the Polish Academy of Sciences Mathematics, 47 147-155 (1999) [C1]
1999 Sims B, Yu H-K, Yuan GX-Z, 'The homotopic invariance for fixed points of set-valued nonexpansive mappings', Josai Mathematical Monograph, 1 55-65 (1999) [C1]
1998 Llorens-Fuster E, Sims B, 'The Fixed Point property in $c_0$', Canadian Mathematical Bulletin, 41 413-422 (1998) [C1]
Citations Web of Science - 7
1998 Garcia-Falset J, Llorens-Fuster E, Sims B, 'Fixed point theory for almost convex functions', Nonlinear Analysis. Theory Methods and Applications, 32 601-698 (1998) [C1]
Citations Web of Science - 10
1997 Falset JG, Sims B, 'Property (M) and the weak fixed point property', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 125 2891-2896 (1997)
DOI 10.1090/S0002-9939-97-03953-1
Citations Scopus - 16Web of Science - 1
1996 Dalby T, Sims B, 'Duality map characterisations for Opial conditions', BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 53 413-417 (1996)
Citations Web of Science - 4
1996 Kirk WA, Sims B, 'Nonlinear isometries in superreflexive spaces', JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 201 247-251 (1996)
DOI 10.1006/jmaa.1996.0253
1996 GarciaFalset J, Sims B, Smyth MA, 'The demiclosedness principle for mappings of asymptotically nonexpansive type', HOUSTON JOURNAL OF MATHEMATICS, 22 101-108 (1996)
Citations Scopus - 9Web of Science - 9
1994 SIMS B, 'A CLASS OF SPACES WITH WEAK NORMAL STRUCTURE', BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 49 523-528 (1994)
Citations Web of Science - 25
1993 KUTZAROVA D, PRUS S, SIMS B, 'REMARKS ON ORTHOGONAL CONVEXITY OF BANACH-SPACES', HOUSTON JOURNAL OF MATHEMATICS, 19 603-614 (1993)
Citations Web of Science - 6
1992 SIMS B, 'THE WEAK KARLOVITZ LEMMA FOR DUAL LATTICES', BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 45 171-176 (1992)
Citations Web of Science - 2
1990 GILES JR, SIMS B, YORKE AC, 'ON THE DROP AND WEAK DROP PROPERTIES FOR A BANACH-SPACE', BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 41 503-507 (1990)
Citations Scopus - 12Web of Science - 15
1989 SIMS B, YOST D, 'LINEAR HAHN-BANACH EXTENSION OPERATORS', PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 32 53-57 (1989)
Citations Web of Science - 19
1986 DAS KC, MAJUMDAR S, SIMS B, 'SUBSETS CHARACTERIZING THE CLOSURE OF THE NUMERICAL RANGE', JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, 40 1-4 (1986)
1985 GILES JR, SIMS B, SWAMINATHAN S, 'A GEOMETRICALLY ABERRANT BANACH-SPACE WITH NORMAL STRUCTURE', BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 31 75-81 (1985)
Citations Scopus - 6Web of Science - 2
1985 MAJUMDAR S, SIMS B, 'SUBSPACES ASSOCIATED WITH BOUNDARY POINTS OF THE NUMERICAL RANGE', JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, 39 21-27 (1985)
1984 BERG ID, SIMS B, 'DENSENESS OF OPERATORS WHICH ATTAIN THEIR NUMERICAL RADIUS', JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, 36 130-133 (1984)
Citations Web of Science - 21
1984 BORWEIN JM, SIMS B, 'NON-EXPANSIVE MAPPINGS ON BANACH-LATTICES AND RELATED TOPICS', HOUSTON JOURNAL OF MATHEMATICS, 10 339-356 (1984)
Citations Web of Science - 29
1983 POLAK T, SIMS B, 'A BANACH-SPACE WHICH IS FULLY 2-ROTUND BUT NOT LOCALLY UNIFORMLY ROTUND', CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 26 118-120 (1983)
DOI 10.4153/CMB-1983-018-7
Citations Web of Science - 3
1983 VANDULST D, SIMS B, 'FIXED-POINTS OF NONEXPANSIVE-MAPPINGS AND TSCHEBYSCHEV CENTERS IN BANACH-SPACES WITH NORMS OF TYPE-(KK)', LECTURE NOTES IN MATHEMATICS, 991 35-43 (1983)
Citations Web of Science - 34
1978 GILES JR, GREGORY DA, SIMS B, 'GEOMETRICAL IMPLICATIONS OF UPPER SEMI-CONTINUITY OF THE DUALITY MAPPING ON A BANACH-SPACE', PACIFIC JOURNAL OF MATHEMATICS, 79 99-109 (1978)
Citations Scopus - 41Web of Science - 40
1978 Giles JR, 'Characterisation of normed linear spaces with Mazur's intersection property', Bull.Aust.Math.Soc., 18 105-123 (1978)
Citations Scopus - 35
1974 SIMS B, 'CONNECTION BETWEEN NUMERICAL RANGE AND SPECTRUM OF AN OPERATOR ON A HILBERT-SPACE', JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 8 57-59 (1974)
Citations Web of Science - 5
Show 39 more journal articles

Conference (14 outputs)

Year Citation Altmetrics Link
2008 Dhompongsa S, Goebel K, Kirk WA, Plubtieng S, Sims B, Suantai S, 'Conference Editors', Fixed Point Theory and its Applications (2008) [E4]
2008 Li G, Sims B, 'T-Demicloseness principle and asymptotic behavior for semigroups of nonexpansive mappings in metric spaces', Fixed Point Theory and its Applications (2008) [E1]
2006 Nathansky HF, De Buen BG, Goebel K, Kirk WA, Sims B, 'Fixed Point Theory and its Applications', Fixed Point Theory and its Applications (2006) [E4]
2006 Dalby T, Sims B, 'Banach lattices and the weak fixed point property', Fixed Point Theory and its Applications (2006) [E1]
2004 Falset JG, Fuster EL, Sims B, 'Proceedings of the International Conference on Fixed Point Theory and Applications', Proceedings of the International Conference on Fixed Point Theory and Applications (2004) [E4]
2004 Mustafa ZY, Sims B, 'Some remarks concerning D - metric spaces', Proceedings of the International Conference on Fixed Point Theory and Applications (2004) [E1]
2003 Sims B, 'Perspectives on metric fixed point theory', Proceedings to be published (2003) [E2]
2003 Sims B, 'Some thoughts on generalized metrics', Proceedings to be published (2003) [E2]
2001 Sims B, Xu HK, Yuang GXZ, 'The homotopic invariance for fixed points of set-valued nonexpansive mappings', FIXED POINT THEORY AND APPLICATIONS, VOL 2 (2001)
2001 Goebel K, Sims B, 'More on minimal invariant sets for nonexpansive mappings', Nonlinear Analysis, Theory, Methods and Applications (2001) [E1]
Citations Web of Science - 3
1999 Sims B, 'Maps which have fixed points for any Banach Space', Proceedings of the Centre for Mathematics and Its Applications (1999) [E1]
1999 Ireland MJ, Kirk WA, Sims B, 'The Leray-Schauder Alternative for Nonexpansive Maps from the Ball Characterize Hilbert Space', Proceedings of the International Conference on Nonlinear analysis and Convex Analysis (1999) [E1]
1999 Sims B, Yu H-K, Yuan GX-Z, 'The homotopic invariance for fixed points of set-valued nonexpansive mappings', The Third Symposium on Nonlinear Analysis (1999) [E1]
Citations Web of Science - 1
1995 Williams MA, Pagnucco M, Foo N, Sims B, 'Determining explanations using transmutations', IJCAI-95 - PROCEEDINGS OF THE FOURTEENTH INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE, VOLS 1 AND 2 (1995)
Citations Web of Science - 2
Show 11 more conferences
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Research Supervision

Number of supervisions

Completed6
Current2

Total current UON EFTSL

PhD0.45

Current Supervision

Commenced Level of Study Research Title / Program / Supervisor Type
2016 PhD An Exploration of Generalised Convexity on Semigroups and Semimodules
PhD (Mathematics), Faculty of Science, The University of Newcastle
Co-Supervisor
2015 PhD Functional Analysis and its Applications
PhD (Mathematics), Faculty of Science, The University of Newcastle
Co-Supervisor

Past Supervision

Year Level of Study Research Title / Program / Supervisor Type
2016 PhD Iterative Projection and Reflection Methods: Theory and Practice
PhD (Mathematics), Faculty of Science, The University of Newcastle
Co-Supervisor
2015 PhD Tree Actions Associated with the Scale of an Automorphism of a Totally Disconnected Locally Compact Group
PhD (Mathematics), Faculty of Science, The University of Newcastle
Co-Supervisor
2015 PhD Expectations over Deterministic Fractal Sets
PhD (Mathematics), Faculty of Science, The University of Newcastle
Co-Supervisor
2014 PhD Nonlinear Analysis in Geodesic Spaces
PhD (Mathematics), Faculty of Science, The University of Newcastle
Principal Supervisor
2011 PhD Connections Between Geometrical and Fixed Point Properties
PhD (Mathematics), Faculty of Science, The University of Newcastle
Principal Supervisor
2005 PhD A New Structure for Generalized Metric Spaces - with Applications to Fixed Point Theory
PhD (Mathematics), Faculty of Science, The University of Newcastle
Principal Supervisor
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Associate Professor Brailey Sims

Position

Conjoint Associate Professor
School of Mathematical and Physical Sciences
Faculty of Science and Information Technology

Focus area

Mathematics

Contact Details

Email brailey.sims@newcastle.edu.au
Phone (02) 4921 5540
Fax (02) 4921 6898

Office

Room V18
Building Mathematics
Location Callaghan
University Drive
Callaghan, NSW 2308
Australia
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