Iterative Computation for Solving the Variational Inequality and the Generalized Equilibrium Problem

An iterative algorithm for solving the variational inequality and the generalized equilibrium problem has been introduced. Convergence result is given

Controllability of second-order neutral functional differential inclusions in Banach spaces

AbstractIn this paper, we prove the controllability of second-order neutral functional differential inclusions in Banach spaces. The result are obtained by using the theory of strongly continuous cosine families and a fixed point theorem for condensing maps due to Martelli

Positive Solutions and Mann Iterative Algorithms for a Nonlinear Three-Dimensional Difference System

The existence of uncountably many positive solutions and Mann iterative approximations for a nonlinear three-dimensional difference system are proved by using the Banach fixed point theorem. Four illustrative examples are also provided

Fixed Point Approximation for Asymptotically Nonexpansive Type Mappings in Uniformly Convex Hyperbolic Spaces

We use a modified S-iterative process to prove some strong and Δ-convergence results for asymptotically nonexpansive type mappings in uniformly convex hyperbolic spaces, which includes Banach spaces and CAT(0) spaces. Thus, our results can be viewed as extension and generalization of several known results in Banach spaces and CAT(0) spaces (see, e.g., Abbas et al. (2012), Abbas et al. (2013), Bruck et al. (1993), and Xin and Cui (2011)) and improve many results in the literature

Viscosity Projection Algorithms for Pseudocontractive Mappings in Hilbert Spaces

An explicit projection algorithm with viscosity technique is constructed for finding the fixed points of the pseudocontractive mapping in Hilbert spaces. Strong convergence theorem is demonstrated. Consequently, as an application, we can approximate to the minimum-norm fixed point of the pseudocontractive mapping

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

Relaxed Extragradient Algorithms for the Split Feasibility Problem

The purpose of this paper is to introduce a new relaxed extragradient algorithms for the split feasibility problem. Our relaxed extragradient algorithm is new and it generalized some results for solving the split feasibility problem

On Positive Solutions and Mann Iterative Schemes of a Third Order Difference Equation

The existence of uncountably many positive solutions and convergence of the Mann iterative schemes for a third order nonlinear neutral delay difference equation are proved. Six examples are given to illustrate the results presented in this paper

Positive Solutions for a Third Order Nonlinear Neutral Delay Difference Equation

The existence, multiplicity, and properties of positive solutions for a third order nonlinear neutral delay difference equation are discussed. Six examples are given to illustrate the results presented in this paper