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In this research paper, we present a novel theoretical technique, referred to as the double Tseng's algorithm with inertial terms, for finding a common solution to two monotone inclusion problems. Developing the double Tseng's algorithm in this manner not only comprehensively expands theoretical knowledge in this field but also provides advantages in terms of step-size parameters, which are beneficial for tuning applications and positively impact the numerical results. This new technique can be effectively applied to solve the problem of image deblurring and offers numerical advantages compared to some previously related results. By utilizing certain properties of a Lipschitz monotone operator and a maximally monotone operator, along with the identity associated with the convexity of the quadratic norm in the framework of Hilbert spaces, and by imposing some constraints on the scalar control conditions, we can achieve weak convergence to a common zero point of the sum of two monotone operators. To demonstrate the benefits and advantages of this newly proposed algorithm, we performed numerical experiments to measure the improvement in the signal–to–noise ratio (ISNR) and the structural similarity index measure (SSIM). The results of both numerical experiments (ISNR and SSIM) demonstrate that our new algorithm is more efficient and has a significant advantage over the relevant preceding algorithms. [ABSTRACT FROM AUTHOR]

In this work, we propose and study an inertial Krasnosel'skii-Mann iterative algorithm with step-size parameters involving nonexpansive mapping to find a solution of a fixed point problem of a nonexpansive mapping in the frame work of Hilbert spaces. Strong convergence of the new proposed algorithm is proved under some useful properties of a nonexpansive mapping and inequalities on real Hilbert spaces together with the appropriate conditions of scalar controls without relying on the concept of viscosity methods. For the applications, we employ the obtained results to find a zero point of some monotone inclusion problems and then apply to solve image restoration problems. For representing the advantage of the new algorithm, the signal to noise ratio (SNR) with various types of blurring operators and some numerical experiments are presented to compare and illustrate the behavior of the new algorithm with numerical results of some previous existing algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study a modified Mann-type algorithm that combines inertial terms for solving common fixed point problems of two countable families of nonexpansive mappings in Hilbert spaces. Under appropriate assumptions on the sequences of parameters, we establish a strong convergence result for the sequence generated by the proposed method in finding a common fixed point of two countable families of nonexpansive mappings. This method can be applied to solve the monotone inclusion problem. Additionally, we employ a modified Mann-type iterative algorithm to address image restoration problems. Furthermore, we present numerical results across different scenarios to demonstrate the superior efficiency of our algorithm compared to existing algorithms. [ABSTRACT FROM AUTHOR]

The purposes of this paper are to establish and study the convergence of a new gradient scheme with penalization terms called rapid gradient penalty algorithm (RGPA) for minimizing a convex differentiable function over the set of minimizers of a convex differentiable constrained function. Under the observation of some appropriate choices for the available properties of the considered functions and scalars, we can generate a suitable algorithm that weakly converges to a minimal solution of the considered constraint minimization problem. Further, we also provide a numerical example to compare the rapid gradient penalty algorithm (RGPA) and the algorithm introduced by Peypouquet [20]. [ABSTRACT FROM AUTHOR]

Abstract The convex feasibility problem (CFP) of finding a point in the nonempty intersection is considered, where is an integer and the 's are assumed to be convex closed subsets of a Banach space . By using hybrid iterative methods, we prove theorems on the strong convergence to a common fixed point for a finite family of relatively nonexpansive mappings. Then, we apply our results for solving convex feasibility problems in Banach spaces.

The purposes of this paper are to introduce and study some existence and convergence theorems for fixed points of a strict pseudo-contraction in the framework of complete CAT(0) spaces. By using available properties in the spaces together with some appropriate conditions of the mapping and under certain assumptions, we can create some suitable sets to be used to construct an iterative projection algorithm to guarantee the existence fixed points for a strict pseudo-contraction. The method allows us to obtain a strong convergence iteration for finding some fixed points of a strict pseudo-contraction in the framework of complete CAT(0) spaces. [ABSTRACT FROM AUTHOR]

In this paper, we establish and study some new existence theorems for a new extended vector variational-like inequality in a Banach space. The results are proved by using the new definition of g - f - η - ϕ - μ-quasimonotone of Stampacchia and of Minty type mappings. The obtained results in this article can be viewed as some new and generalized forms which can be applied to several problems. [ABSTRACT FROM AUTHOR]

We create some new ideas of mappings called quasi-strict ƒ-pseudocontractions. Moreover, we also find the significant inequality related to such mappings and firmly nonexpansive mappings within the framework of Hilbert spaces. By using the ideas of metric ƒ-projection, we propose an iterative shrinking metric ƒ-projection method for finding a common fixed point of a quasi-strict ƒ-pseudocontraction and a countable family of firmly nonexpansive mappings. In addition, we provide some applications of the main theorem to find a common solution of fixed point problems and generalized mixed equilibrium problems as well as other related results. [ABSTRACT FROM AUTHOR]

We provide some new type of mappings associated with pseudocontractions by introducing some actual examples in smooth and strictly convex Banach spaces. Moreover, we also find the significant inequality related to the mappings mentioned in the paper and the mappings defined from generalized mixed equilibrium problems on Banach spaces. We propose an iterative shrinking projection method for finding a common solution of generalized mixed equilibrium problems and fixed point problems of closed and f-quasi-strict pseudo-contractions. Our results hold in reflexive, strictly convex, and smooth Banach spaces with the property (K). The results of this paper improve and extend the corresponding results of Zhou and Gao (2010) and many others [ABSTRACT FROM AUTHOR]

In this paper, we establish two versions of the existence theorems of solutions set of generalized vector variational-like inequalities in fuzzy environment by using two different notions; the first one by using affineness and the second by using the notion of vector O-diagonally convexity. Moreover, an example is established in order to illustrate the main problem. The results of this paper can be viewed as a significant improvement and refinement of several other previously existing known results. [ABSTRACT FROM AUTHOR]

In this paper, we study the solution set of variational like-inequalities (in this sense we are called η-variational inequalities) and introduce the notion of a weak sharp set of solutions to η-variational inequality problem in re exive, strictly convex and smooth Banach space. We also present sufficient conditions for the relevant mapping to be constant on the solutions. Moreover, we characterize the weak sharpness of the solutions of η-variational inequality by primal gap function. [ABSTRACT FROM AUTHOR]