Ivan J. Singer

Ivan J. Singer's AcademicInfluence.com Rankings

Ivan J. Singer

Mathematics

#6567

World Rank

#9073

Historical Rank

Functional Analysis

#42

World Rank

#59

Historical Rank

Applied Mathematics

#232

World Rank

#257

Historical Rank

Measure Theory

#1434

World Rank

#1799

Historical Rank

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Mathematics

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Ivan J. Singer's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces (1970) (792)
Bases in Banach Spaces II (1970) (635)
Abstract Convex Analysis (1997) (321)
CBMS-NSF REGIONAL CONFERENCE SERIES IN APPLIED MATHEMATICS (2010) (292)
The Theory of Best Approximation and Functional Analysis (1974) (210)
High-order finite difference methods for the Helmholtz equation (1998) (172)
Constraint Qualifications for Semi-Infinite Systems of Convex Inequalities (2000) (102)
A perfectly matched layer for the Helmholtz equation in a semi-infinite strip (2004) (102)
Max-plus convex sets and functions (2003) (86)
SIXTH-ORDER ACCURATE FINITE DIFFERENCE SCHEMES FOR THE HELMHOLTZ EQUATION (2006) (81)
Basic sequences and reflexivity of Banach spaces (1962) (74)
A Fenchel-Rockafellar type duality theorem for maximization (1979) (70)
Global Error Bounds for Convex Multifunctions and Applications (1998) (70)
Best coapproximation in normed linear spaces (1979) (67)
Downward Sets and their separation and approximation properties (2002) (67)
A dynamical systems approach to constrained minimization (2000) (65)
On non-equivalent bases and conditional bases in Banach spaces (1964) (63)
Best approximation in max-plus semimodules☆ (2010) (47)
Extensions of functions of 0-1 variables and applications to combinatorial optimization (1985) (41)
Best Approximation by Normal and Conormal Sets (2000) (37)
Duality for Nonconvex Approximation and Optimization (2010) (36)
Some relations between dualities, polarities, coupling functionals, and conjugations (1986) (35)
The distance to a polyhedron (1992) (31)
Max-plus convex sets and max-plus semispaces. II (2007) (31)
Points of diffusion of linear operators and almost diffuse operators in spaces of continuous functions (1965) (30)
A general theory of dual optimization problems (1986) (28)
Dualities between complete lattices (1990) (28)
Generalized Convexity, Functional Hulls and Applications to Conjugate Duality in Optimization (1984) (27)
WEAK CHEBYSHEV SUBSPACES AND ALTERNATION (1980) (27)
Minimization of continuous convex functional on complements of convex subsets of locally convex spaces 1 (1980) (24)
Topologies on lattice ordered groups, separation from closed downward sets and conjugations of type Lau (2003) (23)
Max-plus convex sets and max-plus semispaces. I (2007) (23)
Subdifferentials with respect to dualities (1995) (23)
On set-valued metric projections, Hahn-Banach extension maps, and spherical image maps (1973) (23)
On best approximation of continuous functions (1960) (23)
On convex vectorial optimization in linear spaces (1977) (21)
Uniqueness and strong uniqueness of best approximations by spline subspaces and other subspaces (1982) (20)
On biorthogonal systems and total sequences of functionals. II (1971) (19)
On Set-Valued Metric Projections (1972) (18)
On Banach spaces reflexive with respect to a linear subspace of their conjugate space. II (1962) (17)
Surrogate conjugate functionals and surrogate convexity (1983) (17)
Duality for optimization and best approximation over finite intersections (1998) (17)
On the extension of continuous linear functionals and best approximation in normed linear spaces (1965) (17)
On single-valuedness of convex set-valued maps (1993) (16)
Further Applications of the Additive Min-type Coupling Function (2002) (16)
Bases and quasi-reflexivity of Banach spaces (1964) (16)
Maximization of lower semi-continuous convex functionals on bounded subsets of locally convex spaces. I: Hyperplane theorems (1979) (16)
V -dualities and ⊥-dualities (1991) (16)
Complemented subspaces and Λ systems in banach spaces (1968) (16)
Infimal generators and dualities between complete lattices (1987) (15)
Some characterizations of reflexivity (1975) (15)
A remark on reflexivity and summability (1965) (15)
Generalizations of methods of best approximation to convex optimization in locally convex spaces. II: Hyperplane theorems (1979) (15)
Dualities Associated To Binary Operations On R (1995) (14)
Some further duality theorems for optimization problems with reverse convex constraint sets (1992) (14)
Optimization by level set methods. IV: Generalizations and complements (1982) (14)
Choquet spaces and best approximation (1962) (14)
Some new applications of the Fenchel-Rockafellar duality theorem: Lagrange multiplier theorems and hyperplane theorems for convex optimization and best approximation (1979) (14)
The structure of max-plus hyperplanes (2007) (14)
On Kadec-Klee norms on Banach spaces (1976) (14)
The lower semi-continuous quasi-convex hull as a normalized second conjugate (1983) (14)
The structure of hemispaces in Rn (1988) (13)
Weak compactness, pseudo-reflexivity and quasi-reflexivity (1964) (13)
Lexicographical separation in Rn (1987) (13)
Maximization of lower semi-continuous convex functional on bounded subsets of locally convex spaces. II: Quasi-Lagrangian duality theorems (1980) (13)
Some Relations Between Linear Mappings and Conjugations in Idempotent Analysis (2001) (13)
Surrogate dual problems and surrogate lagrangians (1984) (12)
Dirichlet Finite Solutions of Δu = Pu (1972) (12)
A general theory of surrogate dual and perturbational extended surrogate dual optimization problems (1984) (12)
Optimization by level set methods v:duality theorems for perturbed optimization problems 2 (1984) (11)
Boundary Isomorphism between Dirichlet Finite Solutions of Δu = Pu and Harmonic Functions (1973) (11)
On the problem of non-smoothness of non-reflexive second conjugate spaces (1975) (11)
On shrinking basic sequences in Banach spaces (1971) (10)
Conjugate functionals and level sets (1984) (10)
Boundedly complete $M$-bases and complemented subspaces in Banach spaces (1973) (10)
On Conjugations for Functions with Values in Extensions of Ordered Groups (1997) (10)
Best approximation in normed linear spaces (2011) (10)
Contributions to max-min convex geometry. II Semispaces and convex sets (2008) (9)
Duality theorems for linear systems and convex systems (1980) (9)
Optimization by level set methods vi:generalizations of surrogate type reverse convex duality (1987) (9)
On radiant sets, downward sets, topical functions and sub-topical functions in lattice ordered groups (2004) (9)
Weak* bases in conjugate Banach spaces (1961) (9)
On k-shrinking and k-boundedly complete bases in Banach spaces (1970) (9)
On φ-convexity of convex functions (1998) (9)
Duality theorems for perturbed convex optimization (1981) (8)
Contributions to max-min convex geometry. I. Segments (2008) (8)
Optimization by level set methods. III: Characterizations of solutions in the presence of duality (1982) (8)
Compatible preorders and linear operators on Rn (1991) (7)
Lexicographical order, lexicographical index, and linear operators (1990) (7)
Duality in quasi-convex supremization and reverse convex infimization via abstract convex analysis,and applications to approximation ** (1999) (7)
On a problem of moments of S. Rolewicz (1973) (7)
On a problem of T. J. Rivlin in approximation theory (1969) (6)
Surrogate duality for vector optimization (1987) (6)
Banach Space Theory and its Applications (1983) (6)
On the Cones Associated with Biorthogonal Systems and Bases in Banach Spaces (1969) (6)
On pseudo-complemented subspaces of Banach spaces (1973) (5)
Multi-Order Convexity (1990) (5)
Some characterizations of surrogate dual problems (1992) (5)
Some remarks on domination of sequences (1970) (5)
An extension of D.C. duality theory, with an appendix on ∗-subdifferentials (1997) (5)
A general theory of dual optimization problems. II: On the perturbational dual problem corresponding to an unperturbational dual problem (1989) (5)
On normed linear spaces which are proximinal in every superspace (1973) (5)
On a Theorem of J. D. Weston (1959) (5)
The norm of a linear functional with respect to a non-negative convex functional vanishing at the origin (1980) (4)
Some characterizations of φ-Lagrangian dual problems (1991) (4)
Elementary topical functions on b-complete semimodules over b-complete idempotent semifields (2010) (4)
Acharacterization of Lagrangian dual problems (1990) (4)
Some conjugation formulas and subdifferential formulas of convex analysis revisited (2006) (4)
On the Pontryagin maximum principle for constant-time linear control systems in Banach spaces (1979) (4)
Optimization by Level set Methods. II: Further Duality Formulae in the Case of Essential Constraints (1984) (4)
Extension with larger norm and separation with double support in normed linear spaces (1980) (3)
On biorthogonal systems and total sequences of functionals (1971) (3)
Some further relations between unperturbational and perturbational dual optimization problems (1991) (3)
Multipliers and unconditional convergence of biorthogonal expansions (1971) (3)
Asymptotic Constraint Qualifications and Error Bounds for Semi-Infinite Systems of Convex Inequalities (2001) (3)
A characterization of constant-time linear control systems satisfying the Pontryagin maximum principle (1980) (3)
Topical functions on semimodules and generalizations (2012) (3)
Best Approximation in Normed Linear Spaces by Elements of Arbitrary Linear Subspaces (1970) (3)
The Basis Problem. Some Properties of Bases in Banach Spaces (1970) (2)
A proof of the Dvoretzky-Rogers theorem (1964) (2)
Geometric properties of the norm and basic sequences in Banach spaces (1975) (2)
Abstract subdifferentials and some characterizations of optimal solutions (1988) (2)
On the constants of basic sequences in Banach spaces (1968) (2)
On Banach spaces in which every M-basis is a generalized summation basis (1979) (2)
On minimal sequences of type $l_+$ and bounded biorthogonal systems in Banach spaces (1973) (2)
On dualities between function spaces (1996) (2)
Some extensions of a dual of the Hahn-Banach Theorem, with applications to separation and Helly type theorems (1976) (2)
Extended-valued topical and anti-topical functions on semimodules (2012) (2)
Abstract pontryagin maximum principles for linear systems (1983) (2)
Some general Lagrangian duality theorems (1989) (1)
Uniqueness of best approximations in spaces of continuous functions (1980) (1)
Dual representations of hulls for functions satisfying f (0) = inf f (X\{0}) * (1999) (1)
Remark on a paper of Y. Ikebe (1969) (1)
On the extension of basic sequences to bases (1974) (1)
Some Remarks and Problems on Bases in Banach Spaces (1969) (1)
Some open problems on best approximation in normed linear spaces (1967) (1)
On a theorem of N. K. Bari and I. M. Gelfand (1968) (1)
On the distance of non-reflexive spaces to the collection of all conjugate spaces (1978) (1)
Decompositions (bases of subspaces). Schauder decompositions. Resolutions of the identity. Integral bases (1981) (0)
Errata corring ∨-dualities and ⊥-dualities (1992) (0)
Approximative bases. Quasi-bases. Finite-dimensional expansions of the identity. Commuting approximative bases (1981) (0)
On duality and stability of parametrized optimization problems and related topics (1987) (0)
On nearest points in closed convex sets (1998) (0)
On Suprema of Abstract Convex and Quasi-convex Hulls (2001) (0)
Some characterizations of perturbational dual problems (1994) (0)
Fe b 20 04 Max-plus convex sets and functions (2004) (0)
Optimization: a Journal of Mathematical Programming and Operations Research (2011) (0)
On convex vectorial optimization in linear spaces (1977) (0)
ER-sets. Extended unconditional bases. Transfinite bases. Strongly unconditional integral bases (1981) (0)
Banach space theory and its applications : proceedings of the First Romanian-GDR Seminar held at Bucharest, Romania, August 31-September 6, 1981 (1983) (0)
Strongly Proximinal Sets are Convex (2017) (0)
M-bases. Strong M-bases. Series summable M-bases (1981) (0)
Best approximation and optimization (1984) (0)
Completeness andaw*-topologies (1964) (0)
Minimal sequences. {λi}-linearly independent sequences. Complete minimal sequences. Maximal biorthogonal systems (1981) (0)
Basic sequences. Bibasic systems (1981) (0)
Extended approximative bases. Extended Π-bases. Extended resolutions of the identity (1981) (0)
Deficient basic sequences. Images and inverse images of bases by continuous linear mappings (1981) (0)
Optimization and best approximation (1981) (0)
Banach spaces which do not have the approximation property (1981) (0)
Abstract Convex Analysis (Wiley-Interscience And Canadian Mathematics Series Of Monographs And Texts) By Ivan Singer (2019) (0)
Positiveness of the Reproducing Kernel in the Space PD(R) (1972) (0)
Dual π-bases. Commuting π-bases. Bases with parentheses. Finite-dimensional decompositions (1981) (0)
Duality theorems. Further universal complement properties of the spaces Cp (1981) (0)
T-bases (summation bases). Strongly series summable M-bases. γ-bases (1981) (0)
Transfinite decompositions. Transfinite Schauder decompositions. Ordinal resolutions of the identity (1981) (0)
Best Approximation in Normed Linear Spaces by Elements of Closed Linear Subspaces of Finite Codimension (1970) (0)
On some duality theorems for bases, finite dimensional decompositions and π systems (1974) (0)
Special Classes of Bases in Banach Spaces (1970) (0)
Bases of sets (1981) (0)
Π-bases. π-bases. π1∞-bases. The universal complements Cp (1981) (0)
Duality for Nonconvex Approximation and Optimization With 17 Figures (2013) (0)
Operational bases. Generalized summation bases (1981) (0)
Dirichlet finite solutions of Δ (1972) (0)
Extended biorthogonal systems. Extended M-bases (1981) (0)
Bases with respect to a class of sequences of indices (1981) (0)
Pseudo-bases. Semi-bases (1981) (0)
Lagrangian duality theorems for reverse convex infimization (2000) (0)
On Duality for Quasi-convex Supremization and Reverse Convex Infimization (2001) (0)

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Ivan J. Singer's Published Works

Published Works

Ivan J. Singer's AcademicInfluence.com Rankings