$rho$-Attractive Elements in Modular Function Spaces

In this paper, we introduce the notion of ρ-attractive elements in modular function spaces. A new class of mappings called ρ-k-nonspreading mappings is also introduced. Making a good use of the two notions, we first prove existence results and then some approximation results in the setup of modular function spaces. An example is presented to support the results proved herein.

On nonspreading-type mappings in Hadamard spaces

In this paper, we studied a new class of nonspreading-type mappings more general than the class of strictly pseudononspreading and the class of generalized nonspreading mappings. We state and prove some strong convergence theorems of the Mann-type and Ishikawa-type algorithms for approximating fixed points of our class of mappings in Hadamard spaces.

Convergence theorems for nonspreading mappings and equilibrium problems in Hadamard spaces

In this paper, we introduce a new iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the set of common fixed points of a finite family of nonspreading mappings and a finite family of nonexpansive multivalued mappings in Hadamard space. We state and prove strong and ? convergence theorems of the proposed iterative process. The results obtained in this paper extend and improve some recent known results.

On the generalized asymptotically nonspreading mappings in convex metric spaces

<p>In this article, we propose a new class of nonlinear mappings, namely, generalized asymptotically nonspreading mapping, and prove the existence of fixed points for such mapping in convex metric spaces. Furthermore, we also obtain the demiclosed principle and a delta-convergence theorem of Mann iteration for generalized asymptotically nonspreading mappings in CAT(0) spaces.</p>