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This paper presents and analyzes a new viscosity approximation method with the inertial technique for finding a common fixed point of a countable family of nonexpansive mappings and then its strong convergence theorem is established under some suitable conditions. As a consequence, we employ our proposed algorithm for solving some convex bilevel optimization problems and then apply it for solving regression of a graph of cosine function and classification of some noncommunicable diseases by using the extreme learning machine model. We perform a comparative analysis with other algorithms to demonstrate the performance of our approach. Our numerical experiments confirm that our proposed algorithm outperforms other methods in the literature. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce a new inertial iterative algorithm involving the linesearch rule for the split variational inclusion in real Hilbert spaces. We use two inertial terms to accelerate the convergence speed of the proposed algorithm. Under suitable conditions, we prove its weak convergence theorem. Finally, in applications, we apply our algorithm to image deblurring and data classification problem in predicting diabetes mellitus. [ABSTRACT FROM AUTHOR]

In this article, we consider and investigate a split convex feasibility problem involving two bounded linear operators in Hilbert spaces. We introduce a self-adaptive CQ-type algorithm by selecting the stepsize which is independent of the operator norms and establish a strong convergence result of the proposed algorithm under some mild control conditions. Moreover, we propose a self-adaptive relaxed CQ-type algorithm for solving the problem constrained by sub-level sets of convex functions. A numerical example and an application in compressed sensing are also given to illustrate the convergence behaviour of our proposed algorithms. Our results in this paper improve and generalize some existing results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we focus on solving convex minimization problem in the form of a summation of two convex functions in which one of them is Frecét differentiable. In order to solve this problem, we introduce a new accelerated viscosity forward-backward algorithm with a new linesearch technique. The proposed algorithm converges strongly to a solution of the problem without assuming that a gradient of the objective function is LLipschitz continuous. As applications, we apply the proposed algorithm to classification problems and compare its performance with other algorithms mentioned in the literature. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to invent an accelerated algorithm for the convex minimization problem which can be applied to the image restoration problem. Theoretically, we first introduce an algorithm based on viscosity approximation method with the inertial technique for finding a common fixed point of a countable family of nonexpansive operators. Under some suitable assumptions, a strong convergence theorem of the proposed algorithm is established. Subsequently, we utilize our proposed algorithm to solving a convex minimization problem of the sum of two convex functions. As an application, we apply and analyze our algorithm to image restoration problems. Moreover, we compare convergence behavior and efficiency of our algorithm with other well-known methods such as the forward-backward splitting algorithm and the fast iterative shrinkage-thresholding algorithm. By using image quality metrics, numerical experiments show that our algorithm has a higher efficiency than the mentioned algorithms. [ABSTRACT FROM AUTHOR]

A class of demicontractive mappings was first introduced in [Hicks, T. L. and Kubicek, J. D., On the Mann iteration process in a Hilbert space, J. Math. Anal. Appl., 59 (1977) 498-504 and Maruster, S., The solution by iteration of nonlinear equations in Hilbert spaces, Proc. Amer. Math. Soc., 63 (1977), 69-73] and was first mentioned in the case of multi-valued mappings in [Chidume, C. E., Bello, A. U. and Ndambomve, P., Strong and δ-convergence theorems for common fixed points of a finite family of multivalued demicontractive mappings in CAT(0) spaces, Abstr. Appl. Anal., 2014 (2014), https://doi.org/10.1155/2014/805168 and Isiogugu, F. O. and Osilike, M. O., Convergence theorems for new classes of multivalued hemicontractive-type mappings, Fixed Point Theory Appl., 2014 (2014), https://doi.org/10.1186/1687-1812-2014-93]. The demicontractivity with some weak smoothness conditions ensures only weak convergence of Mann iteration. In 2015, Marus,ter and Rus [Kannan contractions and strongly demicontractive mappings, Creat. Math. Inform., 24 (2015), No. 2, 173-182], introduced a class of strongly demicontractive mappings, and also discussed some relationships between strongly demicontractive mappings and Kannan contractions. In this paper, we introduce a new class of strongly demicontractive multivalued mappings in Hilbert spaces. Strong convergence theorems of Picard and Mann iterative methods for strongly demicontractive multi-valued mappings are established under some suitable coefficients and control sequences. [ABSTRACT FROM AUTHOR]

In this paper, a novel algorithm, called parallel inertial S-iteration forward-backward algorithm (PISFBA) is proposed for finding a common fixed point of a countable family of nonexpansive mappings and convergence behavior of PISFBA is analyzed and discussed. As applications, we apply PISFBA to estimate the weight connecting the hidden layer and output layer in a regularized extreme learning machine. Finally, the proposed learning algorithm is applied to solve regression and data classification problems. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a semi-cyclic Berinde contraction pair on a metric space which is more general than that of semi-cyclic contraction pair defined by Gabeleh and Abkar [Gabeleh, M. and Abkar, A., Best proximity points for semi-cyclic contractive pairs in Banach spaces, Int. Math. Forum, 6 (2011), 2179-2186] and prove an existence result concerning global monomization of best proximity points of this pair. Our main result can be used to obtain a common fixed point theorem of some contractive mappings related to Berinde's contractions without commutative assumption. An example supporting our main result is also given. [ABSTRACT FROM AUTHOR]

In this paper, the existence of best proximity point theorems for two new types of nonlinear non-self mappings in a complete metric space endowed with a directed graph are established. Our main results extend and generalize many known results in the literatures. As a special case of the main results, the best proximity point theorems on partially ordered sets are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a split best proximity point and equilibrium problem, and find a solution of the best proximity point problem such that its image under a given bounded linear operator is a solution of the equilibrium problem. We construct an iterative algorithm to solve such problem in real Hilbert spaces and obtain a weak convergence theorem. Finally, we also give an example to illustrate our result. [ABSTRACT FROM AUTHOR]

In this paper, we prove some fixed point theorems for non-self G-almost contractive mappings in Banach spaces with a directed graph and give some examples to illustrate our main results. The main results in this paper extend and generalize many known results in the literature therein. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to introduce a class of generalized contractions in product spaces in the sense of Prešić. Some examples and fixed point theorems for such introduced mappings in the setting of orbitally complete metric spaces are proved. The results presented here extend and include many existing several results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new type of multi-valued G-contraction mapping on a metric space endowed with a directed graph G and prove an existence theorem for fixed point problems in metric space endowed with a graph. Moreover, we prove fixed point theorems in partially ordered metric spaces by our main result. Some examples illustrating our main results are also present. [ABSTRACT FROM AUTHOR]