generalized mixed equilibrium problem
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2021 ◽  
Vol 18 (9) ◽  
pp. 1620
Author(s):  
Nguyễn Trung Hiếu

 Mục đích của nghiên cứu này là kết hợp khoảng cách Bregman với phương pháp chiếu thu hẹp để giới thiệu một dãy lặp lai ghép mới cho bài toán cân bằng hỗn hợp tổng quát và ánh xạ tựa tiệm cận không giãn hoàn toàn Bregman. Sau đó, với những điều kiện thích hợp, chúng tôi chứng minh rằng dãy lặp được đề xuất hội tụ mạnh đến hình chiếu Bregman của điểm xuất phát lên giao của tập nghiệm bài toán cân bằng hỗn hợp tổng quát và tập điểm bất động của ánh xạ tựa tiệm cận không giãn hoàn toàn Bregman trong không gian Banach phản xạ. Định lí này cải tiến kết quả trong (Alizadeh & Moradlou, 2016) từ ánh xạ lai ghép tổng quát và bài toán cân bằng trong không gian Hilbert sang ánh xạ tựa tiệm cận không giãn hoàn toàn Bregman và bài toán cân bằng hỗn hợp tổng quát trong không gian Banach phản xạ. Kết quả được áp dụng cho bài toán cân bằng hỗn hợp tổng quát và ánh xạ tựa tiệm cận không giãn Bregman trong không gian Banach phản xạ. Đồng thời, một ví dụ được đưa ra để minh họa cho dãy lặp được đề xuất. 


Author(s):  
F. Akutsah ◽  
H. A. Abass ◽  
A. A. Mebawondu ◽  
O. K. Narain

In this paper, we study split generalized mixed equilibrium problem and fixed point problem in real Hilbert spaces with a view to analyze an iterative method for approximating a common solution of split generalized mixed equilibrium problem and fixed point problem of an infinite family of a quasi-nonexpansive multi-valued mappings. The iterative algorithm introduced in this paper is designed in such a way that it does not require the knowledge of the operator norm. We state and prove a strong convergence result of the aforementioned problems and also give application of our main result to split variational inequality problem. Our result complements and extends some related results in literature.


Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 16
Author(s):  
Olawale Kazeem Oyewole ◽  
Oluwatosin Temitope Mewomo

In this paper, we study a schematic approximation of solutions of a split null point problem for a finite family of maximal monotone operators in real Hilbert spaces. We propose an iterative algorithm that does not depend on the operator norm which solves the split null point problem and also solves a generalized mixed equilibrium problem. We prove a strong convergence of the proposed algorithm to a common solution of the two problems. We display some numerical examples to illustrate our method. Our result improves some existing results in the literature.


2019 ◽  
Vol 27 (1) ◽  
Author(s):  
Bashir Ali ◽  
Lawal Umar ◽  
M. H. Harbau

Abstract In this paper, we introduce two iterative algorithms for finding a common element of the set of fixed points of a quasi- ϕ-asymptotically nonexpansive multivalued mapping and the sets of solutions of generalized mixed equilibrium problem in Banach space. Then, we prove strong and weak convergence of the sequences to element in the mentioned set. Our results generalize and improve recent results announced by many authors.


Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 722 ◽  
Author(s):  
Mujahid Abbas ◽  
Yusuf Ibrahim ◽  
Abdul Rahim Khan ◽  
Manuel de la Sen

The purpose of this paper is to introduce a new algorithm to approximate a common solution for a system of generalized mixed equilibrium problems, split variational inclusion problems of a countable family of multivalued maximal monotone operators, and fixed-point problems of a countable family of left Bregman, strongly asymptotically non-expansive mappings in uniformly convex and uniformly smooth Banach spaces. A strong convergence theorem for the above problems are established. As an application, we solve a generalized mixed equilibrium problem, split Hammerstein integral equations, and a fixed-point problem, and provide a numerical example to support better findings of our result.


2018 ◽  
Vol 51 (1) ◽  
pp. 211-232 ◽  
Author(s):  
Lateef Olakunle Jolaoso ◽  
Kazeem Olawale Oyewole ◽  
Chibueze Christian Okeke ◽  
Oluwatosin Temitope Mewomo

Abstract The purpose of this paper is to study a split generalized mixed equilibrium problem and a fixed point problem for nonspreading mappings in real Hilbert spaces.We introduce a new iterative algorithm and prove its strong convergence for approximating a common solution of a split generalized mixed equilibrium problem and a fixed point problem for nonspreading mappings in real Hilbert spaces. Our algorithm is developed by combining a modified accelerated Mann algorithm and a viscosity approximation method to obtain a new faster iterative algorithm for finding a common solution of these problems in real Hilbert spaces. Also, our algorithm does not require any prior knowledge of the bounded linear operator norm. We further give a numerical example to show the efficiency and consistency of our algorithm. Our result improves and compliments many recent results previously obtained in this direction in the literature.


2018 ◽  
Vol 34 (2) ◽  
pp. 191-198
Author(s):  
C. E. CHIDUME ◽  
◽  
M. O. NNAKWE ◽  

Let K be a nonempty closed and convex subset of a uniformly smooth and uniformly convex real Banach space with dual space E∗. In this paper, a new iterative algorithm of Halpern-type is constructed and used to approximate a common element of a generalized mixed equilibrium problem and a common fixed points for a countable family of generalized nonexpansive-type maps. Application of our theorem, in the case of real Hilbert spaces, complements, extends and improves several important recent results. Finally, we give numerical experiments to illustrate the convergence of our sequence.


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