Modified inertial double Mann type iterative algorithm for a bivariate weakly nonexpansive operator

"We introduce a modified inertial double Mann type iterative method to approximate coupled solutions of a bivariate nonexpansive operator T : C x C→ C, where C is a nonempty closed and convex subset of a Hilbert space. The one theorem and complement important old and recent results in coupled fixed point theory. Some appropriate examples to illustrate our results and their generalization are also given. "

Fixed point theorems for countably asymptotically Ф-nonexpansive maps in locally convex spaces and application

In this paper, we introduce the concept of a countably asymptotically ?-nonexpansive operator. In addition, we establish new fixed point results for some countably asymptotically ?-nonexpansive and sequentially continuous maps, fixed-point results of Krasnosel?skii type in locally convex spaces. Moreover, we present Leray-Schauder-type fixed point theorems for countably asymptotically ?-nonexpansive maps in locally convex spaces. Apart from that we show the applicability of our results to the theory of Volterra integral equations in locally convex spaces. The main condition in our results is formulated in terms of the axiomatic measure of noncompactness. Our results improve and extend in a broad sense recent ones obtained in literature.

Mixed Simultaneous Iterative Algorithms for the Extended Multiple-Set Split Equality Common Fixed-Point Problem with Lipschitz Quasi-Pseudocontractive Operators

In this paper, we study a kind of extended multiple-set split equality common fixed-point problem with Lipschitz quasi-pseudocontractive operators, which is an extension of multiple-set split equality common fixed-point problem with quasi-nonexpansive operator. We propose two mixed simultaneous iterative algorithms, in which the selecting of the stepsize does not need any priori information about the operator norms. Furthermore, we prove that the sequences generated by the mixed simultaneous iterative algorithms converge weakly to the solution of this problem. Some numerical results are shown to illustrate the feasibility and efficiency of the proposed algorithms.

Approximating Iterations for Nonexpansive and Maximal Monotone Operators

We present two algorithms for finding a zero of the sum of two monotone operators and a fixed point of a nonexpansive operator in Hilbert spaces. We show that these two algorithms converge strongly to the minimum norm common element of the zero of the sum of two monotone operators and the fixed point of a nonexpansive operator.