Associate Professor Brailey Sims
Conjoint Associate Professor
School of Mathematical and Physical Sciences (Mathematics)
 Email:brailey.sims@newcastle.edu.au
 Phone:(02) 4921 5540
Career Summary
Biography
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; preundergraduate 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 
Publications
For publications that are currently unpublished or inpress, 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 463484 (2013) [B1]


2011 
Borwein JM, Sims B, 'The DouglasRachford algorithm in the absence of convexity', FixedPoint Algorithms for Inverse Problems in Science and Engineering, Springer, New York 93109 (2011) [B1]


2001  Sims AD, Sims B, 'Assessing the minimality of change in belief revision: capacities', Frontiers in Belief Revision, Kluwer Academic Publishers, Dortrecht/Boston/London 163177 (2001) [B1]  
2001  Sims B, 'Examples of fixed point free mappings', Handbook of Metric Fixed Point Theory, Kluwer Academic Publishers, Dortrecht/Boston/London 3548 (2001) [B1]  
2001  Khamsi MA, Sims B, 'Ultramethods in fixed point theory', Handbook of Metric Fixed Point Theory, Kluwer Academic Publishers, Dortrecht/Boston/London 177199 (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 339389 (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 10691081 (2016)  
2015 
Borwein JM, Sims B, Tam MK, 'Norm convergence of realistic projection and reflection methods', Optimization, 64 161178 (2015) [C1] Â© 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] Â© 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.


2014 
Borwein D, Borwein JM, Sims B, 'On the Solution of Linear Mean Recurrences', AMERICAN MATHEMATICAL MONTHLY, 121 486498 (2014) [C1]


2012 
Bacak M, Searston IJ, Sims B, 'Alternating projections in CAT(0) spaces', Journal of Mathematical Analysis and Applications, 385 599607 (2012) [C1]


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 400409 (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 10251038 (2011) [C1]


2010 
Goebel K, Sims B, 'Mean Lipschitzian mappings', Contemporary Mathematics, 513 157167 (2010) [C1]


2009 
Mustafa Z, Sims B, 'Fixed point theorems for contractive mappings in complete Gmetric spaces', Fixed Point Theory and Applications, 9 110 (2009) [C1]


2006 
Dhompongsa S, Kirk WA, Sims B, 'Fixed points of uniformly lipschitzian mappings', Nonlinear AnalysisTheory Methods & Applications, 65 762772 (2006) [C1]


2006 
Mustafa ZY, Sims B, 'A new approach to generalized metric spaces', Journal of Nonlinear and Convex Analysis, 7 289297 (2006) [C1]


2005 
Kirk WA, Sims B, 'An ultrafilter approach to locally almost nonexpansive maps', Nonlinear Analysis, Theory, Methods and Applications, 63 e1241e1251 (2005) [C1]


2003 
Dominguez T, Hudzik H, Lopez G, Mastylo M, Sims B, 'Complete characterizations of KadecKlee properties in Orlicz spaces', HOUSTON JOURNAL OF MATHEMATICS, 29 10271044 (2003)


2003  Tomas D, Genaro L, Henryk H, Mastylo M, Sims B, 'Complete characterization of KadecKlee properties in Orlicz spaces', Houston Journal of Mathematics, 29 10271044 (2003) [C1]  
2002 
Li G, Sims B, 'Fixed point theorems for mappings of asymptotically nonexpansive type', Nonlinear Analysis, 50 10851091 (2002) [C1]


2001  Sims B, Xu HK, 'Locally almost nonexpansive mappings', Communications on Applied Nonlinear Analysis, 8 8188 (2001) [C1]  
2001  Kirk WA, Sims B, 'Uniform normal structure and related notions', Journal of Nonlinear and Convex Analysis, 2 129138 (2001) [C1]  
2000 
Kirk WA, Sims B, Yuan GXZ, 'The KnasterKuratowski and Mazurkiewicz theory in hyperconvex metric spaces and some of its applications', Nonlinear Analysis, 39 611627 (2000) [C1]


2000  Park S, Sims B, 'Remarks on fixed point theorems in hyperconvex spaces', Nonlinear Funct. Anal. & Appl., 5 5164 (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 497513 (1999)


1999  Kirk WA, Sims B, 'Convergence of Picard Iterates of Nonexpansive Mappings', Bulletin of the Polish Academy of Sciences Mathematics, 47 147155 (1999) [C1]  
1999  Sims B, Yu HK, Yuan GXZ, 'The homotopic invariance for fixed points of setvalued nonexpansive mappings', Josai Mathematical Monograph, 1 5565 (1999) [C1]  
1998 
LlorensFuster E, Sims B, 'The Fixed Point property in $c_0$', Canadian Mathematical Bulletin, 41 413422 (1998) [C1]


1998 
GarciaFalset J, LlorensFuster E, Sims B, 'Fixed point theory for almost convex functions', Nonlinear Analysis. Theory Methods and Applications, 32 601698 (1998) [C1]


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, 'TDemicloseness 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 setvalued 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]


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 LeraySchauder 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 HK, Yuan GXZ, 'The homotopic invariance for fixed points of setvalued nonexpansive mappings', The Third Symposium on Nonlinear Analysis (1999) [E1]


Show 11 more conferences 
Research Supervision
Number of supervisions
Total current UON EFTSL
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 CoSupervisor 
2015  PhD 
Functional Analysis and its Applications PhD (Mathematics), Faculty of Science, The University of Newcastle CoSupervisor 
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 CoSupervisor 
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 CoSupervisor 
2015  PhD 
Expectations over Deterministic Fractal Sets PhD (Mathematics), Faculty of Science, The University of Newcastle CoSupervisor 
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 
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
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 