We consider inequalities which incorporate both Jensen and Ostrowski type inequalities for functions with absolutely continuous n-th derivative. We provide applications of these inequalities for divergence measures. In particular, we obtain inequalities involving higher order χ-divergence.

Abstract. Let R be a 2-torsion free ring with identity. In this paper, first we prove that any Jordan left derivation (hence, any left derivation) on the full matrix ringMn(R) (n 2) is identically zero, and any generalized left derivation on this ring is a right centralizer. Next, we show that if R is also a prime ring and n 1, then any Jordan left derivation on the ring Tn(R) of all n×n uppe...

In this paper, we investigate homomorphisms from unital C∗−algebras to unital Banach algebras and derivations from unital C∗−algebras to Banach A−modules related to a Cauchy–Jensen functional inequality. Mathematics subject classification (2010): 39B72, 46H30, 46B06.

moslehian  and mirmostafaee, investigated the fuzzystability problems for the cauchy additive functional equation, the jensen additivefunctional equation and the cubic functional equation in fuzzybanach spaces. in this paper, we investigate thegeneralized hyers–-ulam--rassias stability of the generalizedadditive functional equation with $n$--variables, in fuzzy banachspaces. also, we will show ...

We study convergent (terminating and confluent) presentations of n-categories. Using the notion of polygraph (or computad), we introduce the homotopical property of finite derivation type for n-categories, generalising the one introduced by Squier for word rewriting systems. We characterise this property by using the notion of critical branching. In particular, we define sufficient conditions f...

A difficult step in the derivation of the strong forms of the Cauchy theorem, Green's lemma, and related theorems from the corresponding weak forms is the construction, for a given rectifiable Jordan curve J, of a sequence of Jordan polygons lying interior to / , converging to J", and having uniformly bounded lengths. This note presents what the author believes to be a simpler elementary constr...

Symmetry is repetitive self-similarity. We proved the stability problem by replicating well-known Cauchy equation and Jensen into two variables. In this paper, we Hyers-Ulam of bi-additive functional f(x+y,z+w)=f(x,z)+f(y,w) bi-Jensen 4fx+y2,z+w2=f(x,z)+f(x,w)+f(y,z)+f(y,w).

Abstract In this paper we give some hyperstability and stability results for the Cauchy Jensen functional equations on restricted domains. We provide a simple short proof Brzde?k’s result concerning equation.

Katsaras 1 defined a fuzzy norm on a vector space to construct a fuzzy vector topological structure on the space. Some mathematicians have defined fuzzy norms on a vector space from various points of view 2–4 . In particular, Bag and Samanta 5 , following Cheng and Mordeson 6 , gave an idea of fuzzy norm in such a manner that the corresponding fuzzy metric is of Kramosil and Michálek type 7 . T...