* Correspondence: [email protected]. edu.tw Department of Mathematics, National Changhua University of Education, Changhua, 50058, Taiwan Full list of author information is available at the end of the article Abstract In this paper, we introduced two new classes of nonlinear mappings in Hilbert spaces. These two classes of nonlinear mappings contain some important classes of nonlinear mappings, l...

This paper presents three new families of fractional Sobolev spaces and their accompanying theory in one dimension. The construction are based on a newly developed notion weak derivatives, which natural generalizations the well-established integer order theory. In particular, two one-sided introduced analyzed, they reveal more insights about another family so-called symmetric spaces. Many key t...

‎In this paper‎, ‎we prove some theorems related to properties of‎ ‎generalized symmetric hybrid mappings in Banach spaces‎. ‎Using Banach‎ ‎limits‎, ‎we prove a fixed point theorem for symmetric generalized‎ ‎hybrid mappings in Banach spaces‎. ‎Moreover‎, ‎we prove some weak‎ ‎convergence theorems for such mappings by using Ishikawa iteration‎ ‎method in a uniformly convex Banach space.

We introduced and discussed a second-ordered parametric dual model of complex multi-objective programming problem (P). Moreover, the authors constructed proved weak, strong strictly converse duality theorems by generalized Θ-bonvexity.

We consider a new type of monotone nonexpansive mappings in an ordered Banach space X with partial order . This new class of nonlinear mappings properly contains nonexpansive, firmly-nonexpansive and Suzuki-type generalized nonexpansive mappings and partially extends α-nonexpansive mappings. We obtain some existence theorems and weak and strong convergence theorems for the Mann iteration. Some ...

Abstract. We deal with random processes obtained from a homogeneous random process with independent increments by replacement of the time scale and by multiplication by a norming constant. We prove the convergence in distribution of these processes to Wiener process in the Skorohod space endowed by the topology of uniform convergence. An integral type almost sure version of this limit theorem i...

Functional central limit theorems in L(0, 1) for logarithmic combinatorial assemblies are presented. The random elements argued in this paper are viewed as elements taking values in L(0, 1) whereas the Skorokhod space is argued as a framework of weak convergences in functional central limit theorems for random combinatorial structures in the literature. It enables us to treat other standardized...