An algorithm for finding a common solution for a system of mixed equilibrium problem, quasi-variational inclusion problem and fixed point problem of nonexpansive semigroup

In this paper, the split variational inclusion problem (SVIP) and the system of equilibrium problems (EP) are considered in Hilbert spaces. Inspired by the works of Byrne et al., López et al., Moudafi and Thukur, Sobumt and Plubtieng, Sitthithakerngkiet et al. and Eslamian and Fakhri, a new self-adaptive step size algorithm is proposed to find a common element of the solution set of the problems SVIP and EP. Convergence theorems are established under suitable conditions for the algorithm and application to the common solution of the fixed point problem, and the split convex optimization problem is considered. Finally, the performances and computational experiments are presented and a comparison with the related algorithms is provided to illustrate the efficiency and applicability of our new algorithms.

Download Full-text

Iterative approximation of a common solution of a split generalized equilibrium problem and a fixed point problem for nonexpansive semigroup

Mathematical Sciences ◽

10.1186/2251-7456-7-1 ◽

2013 ◽

Vol 7 (1) ◽

pp. 1 ◽

Cited By ~ 24

Author(s):

Kaleem Raza Kazmi ◽

Shuja Haider Rizvi

Keyword(s):

Fixed Point ◽

Equilibrium Problem ◽

Fixed Point Problem ◽

Nonexpansive Semigroup ◽

Point Problem ◽

Generalized Equilibrium Problem ◽

Iterative Approximation ◽

Common Solution ◽

Generalized Equilibrium ◽

Split Generalized Equilibrium Problem

Download Full-text

A new viscosity-type iteration for a finite family of split variational inclusion and fixed point problems between Hilbert and Banach spaces

Journal of Inequalities and Applications ◽

10.1186/s13660-019-2201-9 ◽

2019 ◽

Vol 2019 (1) ◽

Cited By ~ 1

Author(s):

C. Izuchukwu ◽

F. O. Isiogugu ◽

C. C. Okeke

Keyword(s):

Fixed Point ◽

Fixed Point Theory ◽

Iteration Process ◽

Point Theory ◽

Fixed Point Problem ◽

Finite Family ◽

Variational Inclusion ◽

Inclusion Problem ◽

Point Problem ◽

Common Solution

Abstract In this paper, we introduce a new viscosity-type iteration process for approximating a common solution of a finite family of split variational inclusion problem and fixed point problem. We prove that the proposed algorithm converges strongly to a common solution of a finite family of split variational inclusion problems and fixed point problem for a finite family of type-one demicontractive mappings between a Hilbert space and a Banach space. Furthermore, we applied our results to study a finite family of split convex minimization problems, and also considered a numerical experiment of our results to further illustrate its applicability. Our results extend and improve the results of Byrne et al. (J. Nonlinear Convex Anal. 13:759–775, 2012), Kazmi and Rizvi (Optim. Lett. 8(3):1113–1124, 2014), Moudafi (J. Optim. Theory Appl. 150:275–283, 2011), Shehu and Ogbuisi (Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. 110(2):503–518, 2016), Takahashi and Yao (Fixed Point Theory Appl. 2015:87, 2015), Chidume and Ezeora (Fixed Point Theory Appl. 2014:111, 2014), and a host of other important results in this direction.

Download Full-text