Implicit Iteration Process Research Articles

A novel three-step implicit iteration process for three finite family of asymptotically generalized Φ-hemicontractive mapping in the intermediate sense

A novel three-step implicit iteration process for three finite family of asymptotically generalized Φ-hemicontractive mapping in the intermediate sense

Random fixed point results for generalized asymptotically nonexpansive random operators

In this paper, we define an implicit random iterative process with errors for three finite families of generalized asymptotically nonexpansive random operators. We also prove some convergence theorems using this iteration method in separable Banach spaces.

Convergence analysis of a new implicit iteration process for asymptotically nonexpansive mappings in the intermediate sense in Banach spaces

Convergence analysis of a new implicit iteration process for asymptotically nonexpansive mappings in the intermediate sense in Banach spaces

On Mann-Type Implicit Iteration Process for a Finite Family of α-Hemicontractive Mappings in Hilbert Spaces

The purpose of this article is to study an implicit iteration process for a finite family of α-hemicontractive mappings in Hilbert spaces. Our results extend and generalize the recent results of Husain et al. [12] and Diwan et al. [8] from the classes of hemicontractive and α-demicontractive mappings respectively, to the more general class of α-hemicontractive mappings.

Numerical differentiation for two-dimensional scattered data on arbitrary domain base on Hermite extension with an implicit iteration process

<abstract><p>In this paper, we develop a method for numerical differentiation of two-dimensional scattered input data on arbitrary domain. A Hermite extension approach is used to realize the approximation and a modified implicit iteration method is proposed to stabilize the approximation process. For functions with various smooth conditions, the numerical solution process of the method is uniform. The error estimates are obtained and numerical results show that the new method is effective. The advantage of the method is that it can solve the problem in any domain.</p></abstract>

Bending of flexible round plates

In this paper, schemes for constructing solutions to boundary value problems for static calculation of flexible circular plates with the nonlinear theory of Lyava and Volmyr are presented. From the equations of the equilibrium system of the plates, given in curvilinear coordinates, the system of equilibrium equations for flexible round plates is obtained. Substituting the expressions for the efforts and shearing forces and introducing dimensionless quantities, we obtain a system of quasilinear quantities in displacements. To develop an automated system for static calculation of flexible round plates, we use central finite-difference schemes that approximate derivatives with second-order accuracy, we obtain a system of quasilinear algebraic equations. To test the constructed automatic system for static calculation, the difference equations are reduced to vector form. An implicit iterative process combined with the Gaussian elimination method is applied to the solution of the system of equations. When calculating iterative processes, it continues until the above conditions are met. After determining the required functions by the finite difference method, we calculate the calculated values. Using the obtained numerical results, we will construct their graphs.

The Generalized Implicit Iterative Process for Approximating Fixed Points of Nonexpansive Mappings in CAT(0) Spaces

The aim of this paper is to investigate implicit viscosity iterative algorithm for nonexpansive mappings in the framework of CAT(0) spaces. We prove strong convergence theorems of such algorithm under some suitable assumptions on the sequences of parameters involved therein. We also proved that the presented algorithm is faster than a number of existing iteration processes in literature. Our results extend and improve some recent results of Ahmad et al.[J. Appl. Math. Informatics 35 (5-6)(2017), 423-438] and others.

Generalized Viscosity Implicit Iterative Process for Asymptotically Non-Expansive Mappings in Banach Spaces

In this paper, we propose a generalized viscosity implicit iterative method for asymptotically non-expansive mappings in Banach spaces. The strong convergence theorem of this algorithm is proved, which solves the variational inequality problem. Moreover, we provide some applications to zero-point problems and equilibrium problems. Further, a numerical example is given to illustrate our convergence analysis. The results generalize and improve corresponding results in the literature.

Mandelbrot and Julia Sets via Jungck–CR Iteration With $s$ –Convexity

In today's world, fractals play an important role in many fields, e.g., image compression or encryption, biology, physics, and so on. One of the earliest studied fractal types was the Mandelbrot and Julia sets. These fractals have been generalized in many different ways. One of such generalizations is the use of various iteration processes from the fixed point theory. In this paper, we study the use of Jungck-CR iteration process, extended further by the use of s -convex combination. The Jungck-CR iteration process with s-convexity is an implicit three-step feedback iteration process. We prove new escape criteria for the generation of Mandelbrot and Julia sets through the proposed iteration process. Moreover, we present some graphical examples obtained by the use of escape time algorithm and the derived criteria.

Convergence Rate of Implicit Iteration Process and a Data Dependence Result

The aim of this paper is to introduce an implicit S-iteration processand study its convergence in the framework of W-hyperbolic spaces. We showthat the implicit S-iteration process has higher rate of convergence than implicit Mann type iteration and implicit Ishikawa-type iteration processes. We present a numerical example to support the analytic result proved herein. Finally, we prove a data dependence result for a contractive type mapping using implicit S-iteration process.

Iterative methods with perturbations for the sum of two accretive operators in q-uniformly smooth Banach spaces

In this work, we introduce implicit and explicit iteration processes with perturbations for solving the fixed point problem of nonexpansive mappings and the quasi-variational inclusion problem. We then prove its strong convergence under some suitable conditions. In the last section of the paper, some applications are given also. The results obtained in this paper extend and improve some known others presented in the literature.

Weak Convergence Theorems of Implicit Iterative Process with Errors by Metric Projection Methods and Applications in Signal Analysis

Weak Convergence Theorems of Implicit Iterative Process with Errors by Metric Projection Methods and Applications in Signal Analysis

Approximating common fixed points of Lipschitzian pseudocontraction semigroups

In this paper, we prove a weak convergence theorem of the implicit iteration process for the semigroups of Lipschitz pseudocontractive mappings in uniformly convex Banach spaces with the Opial property.

A one-step implicit iterative process for a finite family of I-nonexpansive mappings in Kohlenbach hyperbolic spaces

The purpose of the present paper is threefold. First, to give definition of I-nonexpansive mappings in a Kohlenbach hyperbolic space. Second, to define a new one-step implicit iterative process. Finally, to establish strong and $$\Delta $$ -convergence theorems for this iterative process in a Kohlenbach hyperbolic space. In addition, an example is provided to validate our result. Our results extend some existing results.

A note on "Implicit iterative process with errors".

In this paper, I introduce an implicit iterative process with mixed errors for two finite family of total asymptotically nonexpansive mappings in a uniformly convex Banach space and prove strong convergence theorems under some conditions. My results improved and extended many know results existing in the literature.

Stability and convergence of a new composite implicit iterative sequence in Banach spaces

The purpose of this paper is to study stability and strong convergence of asymptotically pseudocontractive mappings by using a new composite implicit iteration process in an arbitrary real Banach space. The results in this paper improve and extend the corresponding results in the literature.

Composite Implicit Iteration Process for Asymptotically Hemi-Pseudocontractive Mappings

In Banach space, the composite implicit iterative process for uniformly L- Lipschitzian asymptotically hemi-pesudocontractive mappings are studied, and the sufficient and necessary conditions of strong convergence for the composite implicit iterative process are obtained. AMS subject classifications: 47H09, 47J05, 47J25

Approximation of common fixed points of a finite family of Ø - demicontractive mappings by an implicit iteration method.

We prove that the Implicit Iteration process of Xu and Ori (2001) converges strongly to the commonfixed pointsof a finite family of Ø - demicontractive mappings in real Hilbertand Banachspaces. Our results extend the results of Osilike (2004a) from strictl pseudocontractive maps to the much more general Ø - demicontractive maps;complement and generalize several others in the literature.KEY WORDS AND PHRASES: Ø - Demicontractive Maps, Implicit Iteration Process, Fixed Points,Strong Convergence.

Strong convergence of implicit iteration processes for nonexpansive semigroups in Banach spaces

Let \(C\) be a convex compact subset of a uniformly convex Banach space. Let \(\{T_t\}_{t \geq0}\) be a strongly-continuous nonexpansive semigroup on \(C\). Consider the iterative process defined by the sequence of equations $$x_{k+1} =c_k T_{t_{k+1}}(x_{k+1})+(1-c_k)x_k.$$ We prove that, under certain conditions on \(\{c_k\}\) and \(\{t_k\}\), the sequence \(\{x_k\}_{n=1}^\infty\) converges strongly to a common fixed point of the semigroup \(\{T_t\}_{t \geq0}\). There are known results on convergence of such iterative processes for nonexpansive semigroups in Hilbert spaces and Banach spaces with the Opial property, and also weak convergence results in Banach spaces that are simultaneously uniformly convex and uniformly smooth. In this paper, we do not assume the Opial property or uniform smoothness of the norm.

First-order regularization methods for accretive inclusions in a Banach space

Equations with set-valued accretive operators in a Banach space are considered. Their solutions are understood in the sense of inclusions. By applying the resolvent of the set-valued part of the equation operator, these equations are reduced to ones with single-valued operators. For the constructed problems, a regularized continuous method and a regularized first-order implicit iterative process are proposed. Sufficient conditions for their strong convergence are obtained in the case of approximately specified data.