Complex Variables and Elliptic Equations, ISSN 1747-6933, 10/2016, Volume 61, Issue 10, pp. 1418 - 1433

In this paper, we prove necessary and sufficient conditions for a sense-preserving harmonic function to be absolutely convex in the open unit disc...

uniformly convex | growth theorem | uniformly starlike | Harmonic univalent | Bernardi-type operator | Gaussian hypergeometric functions | coefficient bounds | absolutely convex | Primary: 31A05 | covering theorem | Secondary: 33C05 | MATHEMATICS | Harmonic functions | Harmonics | Operators | Mathematical analysis | Disks | Mapping | Complex variables | Joints

uniformly convex | growth theorem | uniformly starlike | Harmonic univalent | Bernardi-type operator | Gaussian hypergeometric functions | coefficient bounds | absolutely convex | Primary: 31A05 | covering theorem | Secondary: 33C05 | MATHEMATICS | Harmonic functions | Harmonics | Operators | Mathematical analysis | Disks | Mapping | Complex variables | Joints

Journal Article

Numerical algorithms, ISSN 1572-9265, 2018, Volume 82, Issue 3, pp. 909 - 935

In this paper, we study strong convergence of some proximal-type algorithms to a solution of split minimization problem in complete p-uniformly convex metric spaces...

47H10 | Algorithms | Algebra | 49J20 | Numerical Analysis | 49J40 | Computer Science | Numeric Computing | 47H09 | Theory of Computation | MATHEMATICS, APPLIED | INCLUSION PROBLEM | INEQUALITY | ITERATIVE METHOD | Proximal point algorithm | PROJECTION | Resolvent | p-uniformly convex spaces | Split minimization problem | CONVERGENCE | Convex functions | MONOTONE-OPERATORS | FIXED-POINT PROBLEMS

47H10 | Algorithms | Algebra | 49J20 | Numerical Analysis | 49J40 | Computer Science | Numeric Computing | 47H09 | Theory of Computation | MATHEMATICS, APPLIED | INCLUSION PROBLEM | INEQUALITY | ITERATIVE METHOD | Proximal point algorithm | PROJECTION | Resolvent | p-uniformly convex spaces | Split minimization problem | CONVERGENCE | Convex functions | MONOTONE-OPERATORS | FIXED-POINT PROBLEMS

Journal Article

Journal of inequalities and applications, ISSN 1029-242X, 2019, Volume 2019, Issue 1, pp. 1 - 15

Let Y be a uniformly convex multi-Banach space which has not a Frechet differentiable norm...

Kadec-Klee property | AMENABLE SEMIGROUPS | EXISTENCE | MATHEMATICS | RETRACTIONS | MATHEMATICS, APPLIED | Reversible semi-groups | NONEXPANSIVE-MAPPINGS | Asymptotically nonexpansive mapping | Almost orbit | Uniformly convex multi-Banach space | ORBITS | Theorems | Banach spaces | Banach space | Convergence | Ergodic processes | Kadec–Klee property

Kadec-Klee property | AMENABLE SEMIGROUPS | EXISTENCE | MATHEMATICS | RETRACTIONS | MATHEMATICS, APPLIED | Reversible semi-groups | NONEXPANSIVE-MAPPINGS | Asymptotically nonexpansive mapping | Almost orbit | Uniformly convex multi-Banach space | ORBITS | Theorems | Banach spaces | Banach space | Convergence | Ergodic processes | Kadec–Klee property

Journal Article

Commentarii Mathematici Helvetici, ISSN 0010-2571, 2016, Volume 91, Issue 2, pp. 203 - 218

...) and arbitrary unitary representation $\rho$ of $\Gamma$ in a (nonzero) uniformly convex Banach space the vector space $H^2_b(\Gamma;\rho...

Group theory and generalizations | Functional analysis | Acylindrically hyperbolic groups | Uniformly convex Banach space | Second bounded cohomology

Group theory and generalizations | Functional analysis | Acylindrically hyperbolic groups | Uniformly convex Banach space | Second bounded cohomology

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 2011, Volume 61, Issue 1, pp. 117 - 125

In this paper, we define and study some subclasses of analytic functions by using the concept of k -uniformly convexity. Several interesting properties,...

Subordination | Integral operator | Bounded boundary rotation | Conic domains | Elliptic integral | Univalent | [formula omitted]-uniformly convex | Caratheodory functions | K-uniformly convex | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | k-uniformly convex | Operators | Analytic functions | Integrals | Mathematical analysis | Mathematical models | Convexity | Joints

Subordination | Integral operator | Bounded boundary rotation | Conic domains | Elliptic integral | Univalent | [formula omitted]-uniformly convex | Caratheodory functions | K-uniformly convex | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | k-uniformly convex | Operators | Analytic functions | Integrals | Mathematical analysis | Mathematical models | Convexity | Joints

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2013, Volume 401, Issue 1, pp. 1 - 8

Let C be a convex subset of a locally convex space. We provide optimal approximate fixed point results for sequentially continuous maps f:C→C...

Approximate fixed point sequence | Totally bounded set | Approximate fixed point net | Sequentially continuous map | Uniformly continuous map | MATHEMATICS | COMPACT | MATHEMATICS, APPLIED | THEOREMS | PROPERTY | TOPOLOGICAL VECTOR-SPACES | Mathematics - Functional Analysis

Approximate fixed point sequence | Totally bounded set | Approximate fixed point net | Sequentially continuous map | Uniformly continuous map | MATHEMATICS | COMPACT | MATHEMATICS, APPLIED | THEOREMS | PROPERTY | TOPOLOGICAL VECTOR-SPACES | Mathematics - Functional Analysis

Journal Article

Israel Journal of Mathematics, ISSN 0021-2172, 6/2014, Volume 200, Issue 1, pp. 419 - 422

...-Lipschitz embeddings into uniformly convex Banach spaces.

Algebra | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics, general | Mathematics | Group Theory and Generalizations | Applications of Mathematics | MATHEMATICS | MARKOV CONVEXITY | Trees (Graph theory) | Convex functions | Research | Banach spaces | Mathematical research | Functional Analysis | Metric Geometry

Algebra | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics, general | Mathematics | Group Theory and Generalizations | Applications of Mathematics | MATHEMATICS | MARKOV CONVEXITY | Trees (Graph theory) | Convex functions | Research | Banach spaces | Mathematical research | Functional Analysis | Metric Geometry

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2018, Volume 2018, Issue 1, pp. 1 - 15

.... Our main theorem is deduced in metric spaces. As an application, we obtain the corresponding results in uniformly convex Banach spaces using the geometry of the space...

47H10 | Analysis | Optimal approximate solution | Mathematics, general | Best proximity pair | Mathematics | Metric spaces | Applications of Mathematics | 54H10 | Coupling | Uniformly convex Banach space | 54H25 | EXISTENCE | CYCLIC CONTRACTIVE MAPS | MATHEMATICS, APPLIED | MATHEMATICS | FIXED-POINT THEOREMS | MAPPINGS | PROXIMITY POINTS | ORDERED METRIC-SPACES | Couplings | Error analysis | Banach spaces | Banach space | Research

47H10 | Analysis | Optimal approximate solution | Mathematics, general | Best proximity pair | Mathematics | Metric spaces | Applications of Mathematics | 54H10 | Coupling | Uniformly convex Banach space | 54H25 | EXISTENCE | CYCLIC CONTRACTIVE MAPS | MATHEMATICS, APPLIED | MATHEMATICS | FIXED-POINT THEOREMS | MAPPINGS | PROXIMITY POINTS | ORDERED METRIC-SPACES | Couplings | Error analysis | Banach spaces | Banach space | Research

Journal Article

数学物理学报：B辑英文版, ISSN 0252-9602, 2014, Volume 34, Issue 2, pp. 435 - 443

Abstract In this article, we extend the definition of uniformly starlike functions and uni- formly convex functions on the unit disk to the unit ball in C...

星形映照 | 凸函数 | 星像函数 | n次方 | 单位球 | 单位圆盘 | 凸映照 | 判别准则 | uniformly convex mappings | the unit ball | MATHEMATICS | Uniformly starlike mappings

星形映照 | 凸函数 | 星像函数 | n次方 | 单位球 | 单位圆盘 | 凸映照 | 判别准则 | uniformly convex mappings | the unit ball | MATHEMATICS | Uniformly starlike mappings

Journal Article

Journal of Applied Analysis, ISSN 1425-6908, 06/2017, Volume 23, Issue 1, pp. 33 - 38

We investigate classes of -uniformly convex functions which generalize the class introduced by Goodman in 1991...

Starlike functions | order of starlikeness | 30C45 | convex functions | k-uniformly starlike functions | k-uniformly convex functions | Mathematical analysis | Convex analysis

Starlike functions | order of starlikeness | 30C45 | convex functions | k-uniformly starlike functions | k-uniformly convex functions | Mathematical analysis | Convex analysis

Journal Article

数学年刊：B辑英文版, ISSN 0252-9599, 2014, Volume 35, Issue 5, pp. 733 - 742

In this paper, the author studies the coarse embedding into uniformly convex Banach spaces...

一致凸空间 | 嵌入 | 度量空间 | 一致凸Banach空间 | 证明 | 子群 | Coarse embedding | Uniformly convex Banach spaces | 46B20 | 51F99 | Mathematics, general | Mathematics | Applications of Mathematics | Relative hyperbolic groups | MATHEMATICS | EMBEDDABILITY | BAUM-CONNES CONJECTURE | HILBERT-SPACE | RELATIVELY HYPERBOLIC GROUPS | Computer science

一致凸空间 | 嵌入 | 度量空间 | 一致凸Banach空间 | 证明 | 子群 | Coarse embedding | Uniformly convex Banach spaces | 46B20 | 51F99 | Mathematics, general | Mathematics | Applications of Mathematics | Relative hyperbolic groups | MATHEMATICS | EMBEDDABILITY | BAUM-CONNES CONJECTURE | HILBERT-SPACE | RELATIVELY HYPERBOLIC GROUPS | Computer science

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2009, Volume 350, Issue 2, pp. 745 - 757

We prove that if K is a Gruenhage compact space then C ( K ) ∗ admits an equivalent, strictly convex dual norm...

Gruenhage space | Rotund | Strictly convex | Renorming theory | Perfect image | Norm | Tree | Continuous image | MATHEMATICS, APPLIED | SPACES | UNIFORMLY ROTUND NORMS | MATHEMATICS | TREES

Gruenhage space | Rotund | Strictly convex | Renorming theory | Perfect image | Norm | Tree | Continuous image | MATHEMATICS, APPLIED | SPACES | UNIFORMLY ROTUND NORMS | MATHEMATICS | TREES

Journal Article

Communications of the Korean Mathematical Society, ISSN 1225-1763, 2016, Volume 31, Issue 4, pp. 845 - 855

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 06/2015, Volume 426, Issue 2, pp. 1182 - 1191

Let C be a closed, bounded and convex subset of a uniformly convex and uniformly smooth Banach space. Let {Tt...

Nonexpansive semigroup | Fixed point iteration process | Nonexpansive mapping | Uniformly smooth Banach space | Fixed point | Implicit iterative process | MATHEMATICS | COMMON FIXED-POINTS | MATHEMATICS, APPLIED | MEAN ERGODIC THEOREM | OPERATORS | POINTWISE LIPSCHITZIAN MAPPINGS

Nonexpansive semigroup | Fixed point iteration process | Nonexpansive mapping | Uniformly smooth Banach space | Fixed point | Implicit iterative process | MATHEMATICS | COMMON FIXED-POINTS | MATHEMATICS, APPLIED | MEAN ERGODIC THEOREM | OPERATORS | POINTWISE LIPSCHITZIAN MAPPINGS

Journal Article

Inverse problems, ISSN 1361-6420, 2009, Volume 25, Issue 1, pp. 015005 - 015005 (20)

We consider the task of computing an approximate minimizer of the sum of a smooth and a non-smooth convex functional, respectively, in Banach space...

MATHEMATICS, APPLIED | INEQUALITIES | ILL-POSED PROBLEMS | REGULARIZATION | PHYSICS, MATHEMATICAL | OPERATORS | UNIFORMLY CONVEX | Mathematics - Numerical Analysis

MATHEMATICS, APPLIED | INEQUALITIES | ILL-POSED PROBLEMS | REGULARIZATION | PHYSICS, MATHEMATICAL | OPERATORS | UNIFORMLY CONVEX | Mathematics - Numerical Analysis

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 3/2009, Volume 137, Issue 3, pp. 1081 - 1091

Given a Banach space (X,ǁ · ǁ), we study the connection between uniformly convex functions f: X → ℝ bounded above by $\|\cdot \|^{p...

Unit ball | Mathematical functions | Convexity | Banach space | Superreflexive | Convex function | Uniformly convex | Uniformly smooth | uniformly convex | MATHEMATICS | MATHEMATICS, APPLIED | SMOOTHNESS | CONVERGENCE | uniformly smooth | supperreflexive

Unit ball | Mathematical functions | Convexity | Banach space | Superreflexive | Convex function | Uniformly convex | Uniformly smooth | uniformly convex | MATHEMATICS | MATHEMATICS, APPLIED | SMOOTHNESS | CONVERGENCE | uniformly smooth | supperreflexive

Journal Article

Mathematics (Basel), ISSN 2227-7390, 2019, Volume 7, Issue 8, p. 706

In this paper, our aim is to define certain new classes of multivalently spiral-like, starlike, convex and the varied Mocanu-type functions, which are associated with conic domains...

analytic functions | MATHEMATICS | conic domains | close-to-convex functions | uniformly starlike functions | starlike functions | uniformly close-to-convex functions | UNIVALENT | multivalent functions | SUBCLASS

analytic functions | MATHEMATICS | conic domains | close-to-convex functions | uniformly starlike functions | starlike functions | uniformly close-to-convex functions | UNIVALENT | multivalent functions | SUBCLASS

Journal Article

Optimization Methods and Software, ISSN 1055-6788, 01/2020, Volume 35, Issue 1, pp. 21 - 36

In this paper, we extend two important notions, weighted average method and Mann's iterative method, in the study of convex feasibility problem for general maps defined on p-uniformly convex metric spaces. Then we prove the Δ...

Mann's iterative method | Weighted average sequence | Δ-convergence | convex feasibility problem | p-uniformly convex metric space | Metric space | Feasibility studies

Mann's iterative method | Weighted average sequence | Δ-convergence | convex feasibility problem | p-uniformly convex metric space | Metric space | Feasibility studies

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2018, Volume 2018, Issue 1, pp. 1 - 20

... algorithms in uniformly convex and uniformly smooth Banach spaces. The results of this paper improve and extend the previously known ones in the literature.

Systems of nonexpansive operator equations | Analysis | Uniformly smooth | Mathematics, general | Mathematics | Iterative algorithms | Applications of Mathematics | Uniformly convex | Banach space | Solution | MATHEMATICS | MATHEMATICS, APPLIED | FIXED-POINT THEOREMS | CONVERGENCE THEOREMS | METRIC-SPACES | MAPPINGS | Research

Systems of nonexpansive operator equations | Analysis | Uniformly smooth | Mathematics, general | Mathematics | Iterative algorithms | Applications of Mathematics | Uniformly convex | Banach space | Solution | MATHEMATICS | MATHEMATICS, APPLIED | FIXED-POINT THEOREMS | CONVERGENCE THEOREMS | METRIC-SPACES | MAPPINGS | Research

Journal Article

Mathematica Slovaca, ISSN 0139-9918, 08/2019, Volume 69, Issue 4, pp. 825 - 832

Making use of Ruscheweyh -differential operator, we define a new subclass of uniformly convex functions and corresponding subclass of starlike functions with negative coefficients...

starlike function | 30C50 | uniformly convex function | uniformly starlike function | Ruscheweyh | convex function | differential operator | univalent function | Primary 30C45 | Ruscheweyh q-differential operator | MATHEMATICS | ANALYTIC-FUNCTIONS | Operators (mathematics) | Coefficients | Convex analysis | Differential equations

starlike function | 30C50 | uniformly convex function | uniformly starlike function | Ruscheweyh | convex function | differential operator | univalent function | Primary 30C45 | Ruscheweyh q-differential operator | MATHEMATICS | ANALYTIC-FUNCTIONS | Operators (mathematics) | Coefficients | Convex analysis | Differential equations

Journal Article

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