In this paper, a new stochastic self-adaptive subgradient extragradient approximation algorithm incorporated inertial technique is proposed to solve the stochastic pseudomonotone variational inequality problem. The convergence, convergence rate and oracle complexity of the algorithm are investigated. A numerical example illustrates the effectiveness of the new algorithm. The numerical results show that our algorithm is competitive with other related algorithms in the literature [Yang et al. Variance-based modified backward-forward algorithm with line search for stochastic variational inequality problems and its applications. Asia-Pac J Oper Res. 2020;37(3):2050011] and [Wang et al. A self-adaptive stochastic subgradient extragradient algorithm for the stochastic pseudomonotone variational inequality problem with application. Z Angew Math Phys. 2022;73(4):164]. Finally, the main results obtained are applied to solve image restoration problem.

In this paper, an Armijo−Type viscosity algorithm is proposed to solve continuous equilibrium problems without monotonicity on Hadamard manifolds. The iterative sequence generated by the algorithm is shown to converge to a solution of these equilibrium problems on Hadamard manifold under some mild conditions. Meanwhile, the convergence rate of the algorithm is obtained. In addition, the results obtained in this paper is used to solve variational inequality problems and convex minimization problems, and two numerical experiments are provided to verify the effectiveness of the algorithm.

In this article, an iterative algorithm is proposed for solving the split feasibility problem and fixed point problem of Bregman totally quasi-asymptotically nonexpansive mapping in p -uniformly convex and uniformly smooth real Banach spaces. We obtained and proved the strong convergence theorem of the iterative scheme presented. Then, our main result is used to solve split feasibility problem and equilibrium problem.

In this paper, we propose an efficient viscosity type subgradient extragradient algorithm for solving pseudomonotone variational inequality on Hadamard manifolds which is of symmetrical characteristic. Under suitable conditions, we obtain the convergence of the iteration sequence generated by the proposed algorithm to a solution of a pseudomonotone variational inequality on Hadamard manifolds. We also employ our main result to solve a constrained convex minimization problem and present a numerical experiment to illustrate the asymptotic behavior of the algorithm. Our results develop and improve some recent results.

In this paper, under some new appropriate conditions imposed on the parameters and mappings involved in the proximal mapping associated with a general H-monotone operator, its Lipschitz continuity is proved and an estimate of its Lipschitz constant is computed. The main contribution of this work is the establishment of a new equivalence relationship between the graph convergence of a sequence of general strongly H-monotone mappings and their associated proximal mappings, respectively, to a given general strongly H-monotone mapping and its associated proximal mapping by using the notions of graph convergence and proximal mapping concerning a general strongly H-monotone mapping. By employing the concept of proximal mapping relating to general strongly H-monotone mapping, some iterative algorithms are proposed, and as an application of the obtained equivalence relationship mentioned above, a convergence theorem for approximating a common element of the set of solutions of a system of generalized variational inclusions involving general strongly H-monotone mappings and the set of fixed points of an ({an},{bn},ϕ)-total uniformly L-Lipschitzian mapping is proved. It is significant to emphasize that our results are new and improve and generalize many known corresponding results.

In this paper, combining line-search technique with viscosity method, inertial algorithm and subgradient algorithm, we propose a new iterative algorithm that does not involve in projection operators to solve the nonmonotone and non-Lipschitzian equilibrium problem in Hilbert space and obtain the strong convergence theorem. In addition, we also use our main result to the variational inequality and the convex minimization problem, and obtain the corresponding strong convergence theorems.

The main aim of this paper is twofold. Our first objective is to study a new system of generalized multivalued variational-like inequalities in Banach spaces and to establish its equivalence with a system of fixed point problems utilizing the concept of P-η-proximal mapping. The obtained alternative equivalent formulation is used and a new iterative algorithm for finding its approximate solution is suggested. Under some appropriate assumptions imposed on the mappings and parameters involved in the system of generalized multivalued variational-like inequalities, the existence of solution for the system mentioned above is proved and the convergence analysis of the sequences generated by our proposed iterative algorithm is discussed. The second objective of this work is to investigate and analyze the notion M-η-proximal mapping defined in the literature. Taking into account of the assumptions considered for such a mapping, we prove that every M-η-proximal mapping is actually P-η-proximal and is not a new one. At the same time, some comments relating to some existing results are pointed out.

In this work, we suggest a differential variational inequality in reflexive Banach spaces and construct a sequence with a set of constraints and a penalty parameter. We use the penalty method to prove a unique solution to the problem and make suitable assumptions to prove the convergence of the sequence. The proof is based on arguments for compactness, symmetry, pseudomonotonicity, Mosco convergence, inverse strong monotonicity and Lipschitz continuity. Finally, we discuss the boundary value problem for the differential variational inequality problem as an application.

In this paper, an iterative algorithm is introduced to solve the minimization problem and fixed point problem of total asymptotically nonexpansive mappings in CAT(0) spaces and strong convergence theorems and 4-convergence theorems for the above problem are obtained. Finally, the main results are applied to solve the equilibrium problem in CAT(0) spaces. Mathematics Subject Classification: 47H09; 47J25

In this paper, we establish new strong convergence theorems of proposed algorithms under suitable new conditions for the generalized split feasibility problem in Banach spaces. As applications, new strong convergence theorems for equilibrium problems, fixed point problems and split common fixed point problems are also studied. Our new results are distinct from recent results on the topic in the literature.

The purpose of this paper is to propose an algorithm to solve the split feasibility and fixed point problem of quasi-ϕ-nonexpansive mappings in Banach spaces. Without the assumption of semi-compactness on the mappings, it is proved that the sequence generated by the proposed iterative algorithm converges strongly to a common solution of the split feasibility and fixed point problems. As applications, the main results presented in this paper are used to study the convexly constrained linear inverse problem and split null point problem. Finally, a numerical example is given to support our results. The results presented in the paper are new and improve and extend some recent corresponding results.

In this paper, a new algorithm for finding a common element of a split equality fixed point problem for nonexpansive mappings and split equality equilibrium problem in three Banach spaces is introduced. Also, some strong and weak convergence theorems for the proposed algorithm are proved. Finally, the main results obtained in this paper are applied to solve the split equality convex minimization problem.

The purpose of this paper is to propose an iterative algorithm to solve a solution problem which consists of split equilibrium problems and fixed-point problems of quasi-φ -nonexpansive mappings.It is proved that the sequence generated by our proposed iterative algorithm converges strongly to a common solution of the split equilibrium problems and fixed point problems in Banach spaces.As an application, a split optimization problem is investigated.

The purpose of this paper is to propose an algorithm to solve the split equality fixed point problem of nonexpansive mappings in p-uniformly convex and uniformly smooth Banach spaces. The strong convergence theorem of the iterative scheme proposed in this paper is obtained without the assumption of semi-compactenss on the mappings. The results presented in the paper are new and extend some recent corresponding results. Mathematics Subject Classifications: 47H09, 47J25

In this article, we propose an iteration methods for finding a split equality common fixed point of asymptotically nonexpansive semigroups in Banach spaces.The weak and strong convergence theorems of the iteration scheme proposed are obtained.As application, we shall utilize our results to study the split equality variational inequality problems to support the main results.The results presented in the article are new and improve and extend some recent corresponding results.

In this paper, we propose an iteration method for finding a split common fixed point of asymptotically nonexpansive semigroups in the setting of two Banach spaces, and we obtain some weak and strong convergence theorems of the iteration scheme proposed. The results presented in the paper are new and improve and extend some recent corresponding results.

The purpose of this paper is to study the split equality common fixed point problems of quasi-nonexpansive multi-valued mappings in the setting of Banach spaces. For solving this kind of problems, some new iterative algorithms are proposed. Under suitable conditions, some weak and strong convergence theorems for the sequences generated by the proposed algorithm are proved. The results presented in this paper are new which also improve and extend some recent results announced by some authors. c ©2016 All rights reserved.

The purpose of this paper is to introduce and study the split equality variational inclusion problems in the setting of Banach spaces. For solving this kind of problems, some new iterative algorithms are proposed. Under suitable conditions, some strong convergence theorems for the sequences generated by the proposed algorithm are proved. As applications, we shall utilize the results presented in the paper to study the split equality feasibility problems in Banach spaces and the split equality equilibrium problem in Banach spaces. The results presented in the paper are new.