In this research paper, we propose a novel approach termed the inertial subgradient extragradient... more In this research paper, we propose a novel approach termed the inertial subgradient extragradient algorithm to solve bilevel system equilibrium problems within the realm of real Hilbert spaces. Our algorithm is capable of circumventing the necessity for prior knowledge about the Lipschitz constant of the involving bifunction and only computes the minimization of strong bifunctions onto the feasible set that is required. Under appropriate conditions, we establish strong convergence theorems for our proposed algorithms. To validate our algorithms, we illustrate a series of numerical examples. Through these examples, we demonstrate the performance of the algorithms we have put forth in this paper.
In this paper, we propose the new forward backward splitting method for solving variational inequ... more In this paper, we propose the new forward backward splitting method for solving variational inequality problem. The proposed method can be viewed as an extension of the extragradient method by additional projection step at each iteration under the relaxed condition that the mapping is pseudomonotone. The convergence of the proposed method has been proved. Moreover, to show the effectiveness of the proposed method the numerical experiments are performed.
The Journal of Nonlinear Sciences and Applications, 2014
We prove the existence of the unique common fixed point theorems for self mappings which are weak... more We prove the existence of the unique common fixed point theorems for self mappings which are weakly compatible satisfying some contractive conditions on partial metric spaces. Furthermore, we also prove the result on the continuity in the set of common fixed points for self mappings on partial metric spaces.
In this paper, we propose a new algorithm for solving a split equilibrium problem involving nonmo... more In this paper, we propose a new algorithm for solving a split equilibrium problem involving nonmonotone and monotone equilibrium bifunctions in real Hilbert spaces by using a shrinking projection method with a general Armijo line search rule on the ε-subdifferential. We obtain a strong convergence theorem for the new algorithm.
In this paper, we propose two algorithms for finding the solution of a bilevel equilibrium proble... more In this paper, we propose two algorithms for finding the solution of a bilevel equilibrium problem in a real Hilbert space. Under some sufficient assumptions on the bifunctions involving pseudomonotone and Lipschitz-type conditions, we obtain the strong convergence of the iterative sequence generated by the first algorithm. Furthermore, the strong convergence of the sequence generated by the second algorithm is obtained without a Lipschitz-type condition.
In this paper, we introduce two iterative algorithms for finding the solution of the sum of two m... more In this paper, we introduce two iterative algorithms for finding the solution of the sum of two monotone operators by using hybrid projection methods and shrinking projection methods. Under some suitable conditions, we prove strong convergence theorems of such sequences to the solution of the sum of an inverse-strongly monotone and a maximal monotone operator. Finally, we present a numerical result of our algorithm which is defined by the hybrid method.
In this paper, we present an iterative process for finding a common element of solution sets of t... more In this paper, we present an iterative process for finding a common element of solution sets of the variational inequality problem, without a monotone mapping, and fixed point of a nonexpansive mapping. Moreover, we prove a weak convergence theorem by using an our process and give a numerical experiment.
In this research paper, we propose a novel approach termed the inertial subgradient extragradient... more In this research paper, we propose a novel approach termed the inertial subgradient extragradient algorithm to solve bilevel system equilibrium problems within the realm of real Hilbert spaces. Our algorithm is capable of circumventing the necessity for prior knowledge about the Lipschitz constant of the involving bifunction and only computes the minimization of strong bifunctions onto the feasible set that is required. Under appropriate conditions, we establish strong convergence theorems for our proposed algorithms. To validate our algorithms, we illustrate a series of numerical examples. Through these examples, we demonstrate the performance of the algorithms we have put forth in this paper.
In this paper, we propose the new forward backward splitting method for solving variational inequ... more In this paper, we propose the new forward backward splitting method for solving variational inequality problem. The proposed method can be viewed as an extension of the extragradient method by additional projection step at each iteration under the relaxed condition that the mapping is pseudomonotone. The convergence of the proposed method has been proved. Moreover, to show the effectiveness of the proposed method the numerical experiments are performed.
The Journal of Nonlinear Sciences and Applications, 2014
We prove the existence of the unique common fixed point theorems for self mappings which are weak... more We prove the existence of the unique common fixed point theorems for self mappings which are weakly compatible satisfying some contractive conditions on partial metric spaces. Furthermore, we also prove the result on the continuity in the set of common fixed points for self mappings on partial metric spaces.
In this paper, we propose a new algorithm for solving a split equilibrium problem involving nonmo... more In this paper, we propose a new algorithm for solving a split equilibrium problem involving nonmonotone and monotone equilibrium bifunctions in real Hilbert spaces by using a shrinking projection method with a general Armijo line search rule on the ε-subdifferential. We obtain a strong convergence theorem for the new algorithm.
In this paper, we propose two algorithms for finding the solution of a bilevel equilibrium proble... more In this paper, we propose two algorithms for finding the solution of a bilevel equilibrium problem in a real Hilbert space. Under some sufficient assumptions on the bifunctions involving pseudomonotone and Lipschitz-type conditions, we obtain the strong convergence of the iterative sequence generated by the first algorithm. Furthermore, the strong convergence of the sequence generated by the second algorithm is obtained without a Lipschitz-type condition.
In this paper, we introduce two iterative algorithms for finding the solution of the sum of two m... more In this paper, we introduce two iterative algorithms for finding the solution of the sum of two monotone operators by using hybrid projection methods and shrinking projection methods. Under some suitable conditions, we prove strong convergence theorems of such sequences to the solution of the sum of an inverse-strongly monotone and a maximal monotone operator. Finally, we present a numerical result of our algorithm which is defined by the hybrid method.
In this paper, we present an iterative process for finding a common element of solution sets of t... more In this paper, we present an iterative process for finding a common element of solution sets of the variational inequality problem, without a monotone mapping, and fixed point of a nonexpansive mapping. Moreover, we prove a weak convergence theorem by using an our process and give a numerical experiment.
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