We define the multivalued Reich (G, ρ)-contraction mappings on a modular function space. Then we obtain sufficient conditions for the existence of fixed points for such mappings. As an application, we introduce a ρ-valued Bernstein operator on the set of functions f : [0, 1] → Lρ and then give the modular analogue to Kelisky-Rivlin theorem. c ©2016 All rights reserved.

Some limit theorems of the type $\int_{\Omega}f_n dm_n -- --> \int_{\Omega}f dm$ are presented for scalar, (vector), (multi)-valued sequences m_n-integrable functions f_n. The convergences obtained, in vector and multivalued settings, weak or strong sense.

In this note, we establish and improve some results on fixed point theory in topological vector spaces. As a generalization of contraction maps, the concept of quasi contraction multivalued maps on a topological vector space will be defined. Further, it is shown that a quasi contraction and closed multivalued map on a topological vector space has a unique fixed point if it is bounded value.

In this paper, we introduced the notion of a generalized multivalued (α,φ)-almost contractions and establish the existence of fixed point theorems for this class of mapping. The results presented in this paper generalize and extend some recent results in multivalued almost contraction. Also, we show its applications in the Ulam-Hyers stability of fixed point problems for multivalued operators.

Object-oriented Bayesian networks (OOBNs) facilitate the design of large Bayesian networks by allowing Bayesian networks to be nested inside of one another. Weak conditional independence has been shown to be a necessary and sufficient condition for ensuring consistency in OOBNs. Since weak conditional independence plays such an important role in OOBNs, in this paper we establish two useful resu...

In this paper, the concept of generalized Jaggi-Berinde contraction multivalued maps in partially ordered metric spaces is introduced. A fixed point theorem for such maps is established. An example is given to support our main result. We investigate the stability of fixed points for a sequence of generalized Jaggi-Berinde contraction multivalued maps in partially ordered metric spaces. Our resu...

Abstract We introduce a large class of contractive mappings, called Suzuki–Berinde type contraction. show that any contraction has fixed point and characterizes the completeness underlying normed space. A theorem for multivalued mappings is also obtained. These results unify, generalize complement various known comparable in literature.

The purpose of this paper is to present some coincidence point and common  fixed point theorems for multivalued contraction maps in complete fuzzy  metric spaces endowed with a partial order. As an application, we give  an existence theorem of solution for general classes of integral  inclusions by the coincidence point theorem.