It is shown that, in the framework of Gelfand integrable mappings, the Fatou-type lemma for integrably bounded mappings, due to Cornet–Medecin [14] and the Fatou-type lemma for uniformly integrable mappings due to Balder [9], can be generalized to mean norm bounded integrable mappings.

In this paper, we first introduce a class of nonlinear mappings called generic generalized nonspreading which contains the class of generalized nonspreading mappings in a Banach space and then prove an attractive point theorem for such mappings in a Banach space. Furthermore, we prove a mean convergence theorem of Baillon’s type and a weak convergence theorem of Mann’s type for such nonlinear m...

Some interesting properties of dislocated quasi-metric are obtained. Using these properties some fixed point theorems for contractions and Kannan mappings are derived dropping continuity condition imposed by F. M. Zeyada et al (The Arabian Journal for Science and Engineering, Volume 31, Number 1A, (2005), 111–114), C. T. Aage and J. N. Salunke (Applied Mathematical Sciences, Vol. 2,59 (2008) 29...

In 1940 S.M. Ulam proposed the famous Ulam stability problem. In 1941 D.H. Hyers solved the well-known Ulam stability problem for additive mappings subject to the Hyers condition on approximately additive mappings. In this paper we introduce generalized additive mappings of Jensen type mappings and establish new theorems about the Ulam stability of additive and alternative additive mappings.

We define the concept of generalized ϕ-pair mappings and prove some common fixed point theorems for this type of mappings. Our results generalize some recent results.

The concept of tangential for single-valued mappings is extended to multivalued mappings and used to prove the existence of a common fixed point theorem of Gregus type for four mappings satisfying a strict general contractive condition of integral type. Consequently, several known fixed point results generalized and improved the corresponding recent result of Pathak and Shahzad 2009 and many au...

In this paper we study the existence of common fixed point for r-compatible mapping satisfying a generalized quasi contraction condition integral type in modular spaces Our results extend and generalize Beygmohammadi Razani [4] Moradi [25].

This study is devoted to investigate the problem whether existence and uniqueness of integral type contraction mappings on orthogonal metric spaces. At end, we give an example illustrative our main result.

Huang and Zhang 1 generalized the notion of metric space by replacing the set of real numbers by ordered Banach space, deffined a cone metric space, and established some fixed point theorems for contractive type mappings in a normal cone metric space. Subsequently, several other authors 2–5 studied the existence of common fixed point of mappings satisfying a contractive type condition in normal...

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 ...