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1
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Approximating common fixed points of asymptotically nonexpansive mappings by composite algorithm in Banach spaces

100%
Qin X., Su Y., Shang M.
Open Mathematics
|
2007
|
tom 5
|
nr 2
345-357
EN
Let E be a uniformly convex Banach space and K a nonempty convex closed subset which is also a nonexpansive retract of E. Let T 1, T 2 and T 3: K → E be asymptotically nonexpansive mappings with {k n}, {l n} and {j n}. [1, ∞) such that Σn=1∞(k n − 1) < ∞, Σn=1∞(l n − 1) < ∞ and Σn=1∞(j n − 1) < ∞, respectively and F nonempty, where F = {x ∈ K: T 1x = T 2x = T 3 x} = x} denotes the common fixed points set of T 1, T 2 and T 3. Let {α n}, {α′ n} and {α″ n} be real sequences in (0, 1) and ∈ ≤ {α n}, {α′ n}, {α″ n} ≤ 1 − ∈ for all n ∈ N and some ∈ > 0. Starting from arbitrary x 1 ∈ K define the sequence {x n} by $$\left\{ \begin{gathered} z_n = P(\alpha ''_n T_3 (PT_3 )^{n - 1} x_n + (1 - \alpha ''_n )x_n ), \hfill \\ y_n = P(\alpha '_n T_2 (PT_2 )^{n - 1} z_n + (1 - \alpha '_n )x_n ), \hfill \\ x_{n + 1} = P(\alpha _n T_1 (PT_1 )^{n - 1} y_n + (1 - \alpha _n )x_n ). \hfill \\ \end{gathered} \right.$$ (i) If the dual E* of E has the Kadec-Klee property then {x n} converges weakly to a common fixed point p ∈ F; (ii) If T satisfies condition (A′) then {x n} converges strongly to a common fixed point p ∈ F.
2
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Existence of a common solution for a system of nonlinear integral equations via fixed point methods inb-metric spaces

100%
Yamaod O., Sintunavarat W., Je Cho Y.
Open Mathematics
|
2016
|
tom 14
|
nr 1
128-145
EN
In this paper we introduce a property and use this property to prove some common fixed point theorems in b-metric space. We also give some fixed point results on b-metric spaces endowed with an arbitrary binary relation which can be regarded as consequences of our main results. As applications, we applying our result to prove the existence of a common solution for the following system of integral equations: x (t) =  ∫ a b K 1  (t,r,x(r)) dr, x (t) =  ∫ a b K 2  (t,r,x(r)) dr,       $$\matrix {x (t) = \int \limits_a^b {{K_1}} (t, r, x(r))dr, & & x(t) = \int \limits_a^b {{K_2}}(t, r, x(r))dr,} $$ where a, b ∈ ℝ with a < b, x ∈ C[a, b] (the set of continuous real functions defined on [a, b] ⊆ ℝ) and K1, K2 : [a, b] × [a, b] × ℝ → ℝ are given mappings. Finally, an example is also given in order to illustrate the effectiveness of such result.
3
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The minimal displacement problem in the space l ∞

100%
Bolibok K.
Open Mathematics
|
2012
|
tom 10
|
nr 6
2211-2214
EN
We give a lower bound for the minimal displacement characteristic in the space l ∞.
4
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Construction of a common element for the set of solutions of fixed point problems and generalized equilibrium problems in Hilbert spaces

76%
Khan M. A. A.
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
|
2016
|
tom 15
EN
In this paper, we propose and analyse an iterative algorithm for the approximation of a common solution for a finite family of k-strict pseudocontractions and two finite families of generalized equilibrium problems in the setting of Hilbert spaces. Strong convergence results of the proposed iterative algorithm together with some applications to solve the variational inequality problems are established in such setting. Our results generalize and improve various existing results in the current literature.
5
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Cyclic pairs and common best proximity points in uniformly convex Banach spaces

76%
Gabeleh M., Julia Mary P., Eldred Eldred A. A., Olela Otafudu O.
Open Mathematics
|
2017
|
tom 15
|
nr 1
711-723
EN
In this article, we survey the existence, uniqueness and convergence of a common best proximity point for a cyclic pair of mappings, which is equivalent to study of a solution for a nonlinear programming problem in the setting of uniformly convex Banach spaces. Finally, we provide an extension of Edelstein’s fixed point theorem in strictly convex Banach spaces. Examples are given to illustrate our main conclusions.
6
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Non-self mappings in modular spaces and common fixed point theorems

64%
Razani A., Rakočević V., Goodarzi Z.
Open Mathematics
|
2010
|
tom 8
|
nr 2
357-366
EN
The aim of this paper, is to introduce the convex structure (specially, Takahashi convex structure) on modular spaces. Moreover, we are interested in proving some common fixed point theorems for non-self mappings in modular space.
7
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Convergence and stability of generalizedφ-weak contraction mapping inCAT(0) spaces

64%
Kim K. S.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1063-1074
EN
The aim of this paper is to prove some fixed point results for generalized φ-weak contraction mapping and study a new concept of stability which is called comparably almost T-stable by using iterative schemes in CAT(0) spaces.
8
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Generalized bi-quasi-variational inequalities for quasi-pseudo-monotone type II operators on compact sets

52%
Chowdhury M., Tan K.-K.
Open Mathematics
|
2010
|
tom 8
|
nr 1
158-169
EN
In this paper, the authors prove some existence results of solutions for a new class of generalized bi-quasi-variational inequalities (GBQVI) for quasi-pseudo-monotone type II and strongly quasi-pseudo-monotone type II operators defined on compact sets in locally convex Hausdorff topological vector spaces. In obtaining these results on GBQVI for quasi-pseudo-monotone type II and strongly quasi-pseudo-monotone type II operators, we shall use Chowdhury and Tan’s generalized version [3] of Ky Fan’s minimax inequality [7] as the main tool.
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