Wyniki wyszukiwania - BazTech

1

Inertial iterative method with self-adaptive step size for finite family of split monotone variational inclusion and fixed point problems in Banach spaces

Ogwo Grace N., Alakoya Timilehin O., Mewomo Oluwatosin T.

Demonstratio Mathematica

|

2022

|

Vol. 55, nr 1

193--216

EN

In this paper, we propose and study a new inertial iterative algorithm with self-adaptive step size for approximating a common solution of finite family of split monotone variational inclusion problems and fixed point problem of a nonexpansive mapping between a Banach space and a Hilbert space. This method combines the inertial technique with viscosity method and self-adaptive step size for solving the common solution problem. We prove a strong convergence result for the proposed method under some mild conditions. Moreover, we apply our result to study the split feasibility problem and split minimization problem. Finally, we provide some numerical experiments to demonstrate the efficiency of our method in comparison with some well-known methods in the literature. Our method does not require prior knowledge or estimate of the operator norm, which makes it easily implementable unlike so many other methods in the literature, which require prior knowledge of the operator norm for their implementation.

2

Generalized common fixed point theorem for generalized hybrid mappings in Hilbert spaces

Kondo Atsumasa

Demonstratio Mathematica

|

2022

|

Vol. 55, nr 1

752--759

EN

In this article, we prove a common fixed point theorem for commutative nonlinear mappings that jointly satisfy a certain condition. From the main theorem, a common fixed point theorem for commutative generalized hybrid mappings is derived as a special case. Our novel approach significantly expands the applicable range of mappings for well-known fixed point theorems to be effective. Examples are presented to explicitly illustrate this contribution.

3

Implicit functions under fixed point consideration in Probabilistic Menger Spaces

Murthy P. P., Prasad K. N. V. V. V., Majumdar J.

Fasciculi Mathematici

|

2020

|

nr 63

45--61

EN

In the present paper, we have introduced a pair of weakly-biased maps in the Probabilistic Menger Spaces under the implicit relation. Our results proved herein is the partial extension and mild improvement of the results due to Imdad, Tanveer and Hasan [10]. We have discussed an example in support of our main theorem.

4

An iterative algorithm for the system of split mixed equilibrium problem

Karahan Ibrahim, Jolaoso Lateef Olakunle

Demonstratio Mathematica

|

2020

|

Vol. 53, nr 1

309--324

EN

In this article, a new problem that is called system of split mixed equilibrium problems is introduced. This problem is more general than many other equilibrium problems such as problems of system of equilibrium, system of split equilibrium, split mixed equilibrium, and system of split variational inequality. A new iterative algorithm is proposed, and it is shown that it satisfies the weak convergence conditions for nonexpansive mappings in real Hilbert spaces. Also, an application to system of split variational inequality problems and a numeric example are given to show the efficiency of the results. Finally, we compare its rate of convergence other algorithms and show that the proposed method converges faster.

5

Normal structure in modulated topological vector spaces

Kozlowski Wojciech M.

Commentationes Mathematicae

|

2020

|

Vol. 60, No. 1/2

1--11

EN

Following the author’s recent paper On modulated topological vector spaces and applications, Bull. Aust. Math. Soc. (2020), we discuss a notion of modulated topological vector spaces, that generalise, among others, Banach spaces and modular function spaces. The interest in modulars reflects the fact that the notions of “norm like” but “non-euclidean” (i.e., possibly without the triangle property and non-necessarily homogenous) constructs to measure a level of proximity between complex objects have been used extensively in statistics and applied in many empirical scientific projects requiring an objective differentiation between several classes of objects, efficiently applied in many modern clustering and Artificial Intelligence (AI) related computer algorithms. As an example of application, we prove some results, which extend fixed point theorems from the above mentioned paper, by moving from the setting of admissible sets to a simpler and more general setup, which covers also closed bounded sets. The theory of modulated topological vector spaces provides a very minimalistic framework, where powerful geometrical, fixed point, approximation and optimisation theorems are valid under a bare minimum of assumptions.

6

Common fixed points of a three-step iteration with errors of asymptotically quasi-nonexpansive nonself-mappings in the intermediate sense in Banach spaces

Okeke G A, Olaleru J. O.

Fasciculi Mathematici

|

2014

|

Nr 52

93--115

EN

In this paper, we extend the results of Inprasit and Wattanataweekul [7] to the class of asymptotically quasi-nonexpansive nonself-mappings in the intermediate sense. We prove some strong convergence theorems for asymptotically quasi-nonexpansive nonself-mappings in the intermediate sense using a three-step iterative method for finding a common element of the set of solutions of a generalized mixed equilibrium problem and the set of common fixed points of a finite family of nonexpansive mappings in a real Hilbert space. Our results extends, improves, unifies and generalizes the results of [13], [25] and [27].

7

Some remarks on a fixed point property for multivalued mapping

Kapeluszny J.

Journal of Mathematics and Applications

|

2010

|

Vol. 32

47-52

EN

In [5] T. Dominguez Benavides and B. Gavira proved that Banach spaces with [wzór] satisfy the fixed point property for nonexpansive compact convex valued multivalued mappings. We give some simplification of the proof of this theorem.

8

Convergence of Picard iterates of nonexpansive mappings

Kirk W., Sims B.

Bulletin of the Polish Academy of Sciences. Mathematics

|

1999

|

Vol. 47, no 2

147-155

EN

Let X be a Banach space, C a closed subset of X, and T : C --> C a nonexpansive mapping. Conditions are given which assure that if the fixed point set F(T) of T has nonempty interior then the Picard iterates of the mapping T always converge to a point of F(T). If T is asymptotically regular, it suffices to assume that the closed subsets of X are densely proximinal and that nested spheres in X have compact interfaces. Such spaces include, among others, those which have Rolewicz's property ([beta]). If X has strictly convex norm the asymptotic regularity assumption can be dropped and the nested sphere property holds trivially. Consequently the result holds for all reflexive locally uniformly convex spaces.