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Computers & mathematics with applications (1987), ISSN 0898-1221, 2011, Volume 62, Issue 11, pp. 4007 - 4014
Let C be a nonempty, closed and convex subset of a real Hilbert space H . Let T i : C → H , i = 1 , 2 , … , N , be a finite family of generalized asymptotically nonexpansive mappings... 
Monotone mappings | Strong convergence | Variational inequality problems | Equilibrium problems | Relatively quasi-nonexpansive mappings | WEAK | MATHEMATICS, APPLIED | FINITE FAMILY | THEOREMS | ALGORITHM | FIXED-POINTS | Asymptotic properties | Mathematical analysis | Nonlinearity | Hilbert space | Mathematical models | Mapping | Iterative methods | Convergence
Journal Article
Fixed Point Theory and Applications, ISSN 1687-1820, 12/2013, Volume 2013, Issue 1, pp. 1 - 43
Journal Article
Studia Mathematica, ISSN 0039-3223, 2005, Volume 171, Issue 3, pp. 283 - 293
The notion of proximal normal structure is introduced and used to study mappings that are "relatively nonexpansive" in the sense that they are defined on the union of two subsets A and B of a Banach... 
Fixed points | Proximal normal structure | Proximal points | Relatively nonexpansive mappings | MATHEMATICS | proximal normal structure | proximal points | fixed points | relatively nonexpansive mappings
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 2007, Volume 67, Issue 6, pp. 1958 - 1965
In this paper, we prove two strong convergence theorems of modified Ishikawa iteration and modified Halpern iteration for relatively nonexpansive mappings in a Banach space... 
Asymptotic fixed point | Relatively nonexpansive mapping | Generalized projection | Nonexpansive mapping | MATHEMATICS | asymptotic fixed point | MATHEMATICS, APPLIED | ITERATION METHOD | WEAK-CONVERGENCE | nonexpansive mapping | EXAMPLE | relatively nonexpansive mapping | generalized projection | FIXED-POINTS
Journal Article
Numerical functional analysis and optimization, ISSN 1532-2467, 2015, Volume 37, Issue 1, pp. 80 - 91
... ∪ B → A ∪ B be a continuous and asymptotically relatively nonexpansive map. We prove that there exists x ∈ A ∪ B such that ||x − Tx|| = dist(A, B) whenever T(A) ⊆ B, T(B... 
Asymptotically nonexpansive maps | property UC | best proximity points | relatively nonexpansive maps | proximal pairs | Asymptoticallynonexpansive maps | proximalpairs | relativelynonexpansive maps | bestproximitypoints | EXISTENCE | MATHEMATICS, APPLIED | CONVERGENCE | Theorems | Proximity | Rectangles | Asymptotic properties | Mapping | Functional analysis | Banach space | Optimization | Mathematics - Functional Analysis
Journal Article
Fixed Point Theory and Applications, ISSN 1687-1820, 12/2011, Volume 2011, Issue 1, pp. 1 - 15
...-nonexpansive mapping and in the solution set of an equilibrium problem. Strong convergence theorems of common elements are established in a uniformly smooth and strictly convex Banach space which has the Kadec-Klee property... 
Equilibrium problem | Lower semi-continuous | Mathematical and Computational Biology | Analysis | Generalized projection | Mathematics, general | Asymptotically quasi- ϕ -nonexpansive mapping | Mathematics | Relatively non-expansive mapping | Topology | Applications of Mathematics | Differential Geometry | Asymptotically quasi-φ-nonexpansive mapping | Asymptotically quasi-ϕ-nonexpansive mapping
Journal Article
Journal of Inequalities and Applications, ISSN 1025-5834, 12/2015, Volume 2015, Issue 1, pp. 1 - 13
...) for quasi-nonexpansive mappings. In contrast with related processes, our method does not require any demiclosedness principle condition imposed on the involved operators belonging to the wide class of quasi-nonexpansive operators... 
weak relatively nonexpansive mapping | 47H10 | fixed point | Analysis | viscosity approximation method | Mathematics, general | Mathematics | 37C25 | Applications of Mathematics | strong convergence | EXISTENCE | MATHEMATICS, APPLIED | ACCRETIVE-OPERATORS | FAMILY | VARIATIONAL-INEQUALITIES | MATHEMATICS | THEOREMS | CONVERGENCE | EQUILIBRIUM PROBLEMS | FIXED-POINT PROBLEMS | ZEROS | Viscosity | Operators | Algorithms | Approximation | Mathematical analysis | Inequalities | Mapping | Banach space | Convergence
Journal Article
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 2011, Volume 62, Issue 12, pp. 4656 - 4666
Journal Article
Journal of Approximation Theory, ISSN 0021-9045, 2007, Volume 149, Issue 2, pp. 103 - 115
In this paper, we establish strong convergence theorems for a common fixed point of two relatively nonexpansive mappings in a Banach space by using the hybrid method in mathematical programming... 
Asymptotic fixed point | Common fixed point | Relatively nonexpansive mapping | Generalized projection | Nonexpansive mapping | MATHEMATICS | asymptotic fixed point | APPROXIMATION | WEAK-CONVERGENCE | common fixed point | nonexpansive mapping | EXAMPLE | relatively nonexpansive mapping | OPERATORS | generalized projection
Journal Article
The Journal of Analysis, ISSN 0971-3611, 6/2018, Volume 26, Issue 1, pp. 9 - 14
... (Numer Funct Anal Optim 37:80–91, 2016) fixed point theorem for asymptotically relatively nonexpansive mappings. 
Asymptotically relatively nonexpansive mapping | UC-property | P -property | Mathematics | Abstract Harmonic Analysis | 47H10 | Fourier Analysis | Functional Analysis | Special Functions | Analysis | 47H09 | Fixed points | Measure and Integration
Journal Article
Nonlinear analysis, ISSN 0362-546X, 2009, Volume 70, Issue 1, pp. 45 - 57
In this paper, we introduce two iterative sequences for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of an equilibrium problem in a Banach space... 
Convergence theorem | Resolvent | Equilibrium problem | Banach space | Relatively nonexpansive mapping | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Fixed Point Theory and Applications, ISSN 1687-1820, 12/2011, Volume 2011, Issue 1, pp. 1 - 9
In this paper, an iterative sequence for relatively nonexpansive multi-valued mappings by using the notion of generalized projection is introduced, and then weak and strong convergence theorems are proved... 
relatively nonexpansive | iterative sequence | Mathematical and Computational Biology | fixed point | Analysis | Mathematics, general | Mathematics | multi-valued mapping | Applications of Mathematics | Topology | Differential Geometry | Multi-valued mapping | Fixed point | Iterative sequence | Relatively nonexpansive | MATHEMATICS | OPERATORS | Usage | Fixed point theory | Convergence (Mathematics) | Banach spaces | Point mappings (Mathematics) | Methods
Journal Article
Journal of inequalities and applications, ISSN 1029-242X, 2014, Volume 2014, Issue 1, pp. 1 - 14
.... Then we investigate the structure of minimal sets of cyclic relatively nonexpansive mappings in the setting of convex metric spaces... 
cyclic relatively nonexpansive mapping | convex metric space | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | best proximity point | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | CONVERGENCE | PROXIMITY POINT THEOREMS | Theorems | Mapping | Proximity | Metric space | Inequalities
Journal Article
Optimization Letters, ISSN 1862-4472, 2/2014, Volume 8, Issue 2, pp. 533 - 542
Let $$C$$ be a nonempty closed convex subset of a real Hilbert space $$H$$ . Let $$\{T_i\}^{\infty }_{i=1}:C\rightarrow H$$ be an infinite family of generalized asymptotically nonexpansive nonself mappings... 
Monotone mappings | Strong convergence | Computational Intelligence | Equilibrium problems | Operations Research/Decision Theory | Numerical and Computational Physics | 47H09 | Mathematics | Variational inequality problems | 47J25 | Optimization | Relatively quasi-nonexpansive mappings | WEAK | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | FINITE FAMILY | THEOREMS | FIXED-POINTS
Journal Article
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