and Applied Analysis 3 for all μ ∈ T1 and all x, y ∈ A. If there exists an L < 1 such that φ x, y ≤ 2Lφ x/2, y/2 for all x, y ∈ A, then there exists a unique C∗-algebra homomorphism H : A → B such that ∥ ∥f x −H x ∥∥B ≤ L 1 − L x, 0 2.5 for all x ∈ A. Proof. It follows from φ x, y ≤ 2Lφ x/2, y/2 that lim j→∞ 2−jφ ( 2x, 2y ) 0 2.6 for all x, y ∈ A. Consider the set X : {g : A −→ B} 2.7 and intro...

In this paper, we solve a new Jensen type m-dimensional multiplicative inverse functional equation and then its various stability problems in the setting of non-negative real numbers non-Archimedean spaces via fixed point method. The dealt study is linked with famous relationship between arithmetic harmonic mean m values. role very significant many other fields such as traffic flow theory, indu...

New inequalities for the general case of convex functions defined on linear spaces which improve the famous Jensen’s inequality are established. Particular instances in the case of normed spaces and for complex and real n-tuples are given. Refinements of Shannon’s inequality and the positivity of Kullback-Leibler divergence are obtained.

In this paper we generalize the inequality MJn (f,x,q) ≥ Jn (f,x,p) ≥ mJn (f,x,q) where Jn (f,x,p) = n ∑ i=1 pif (xi)− f ( n ∑ i=1 pixi ) , obtained by S.S. Dragomir for convex functions. We provide cases where we can improve the bounds m and M for convex functions, and also, we show that for the class of superquadratic functions nonzero lower bounds of Jn (f,x,p)− mJn (f,x,q) and nonzero upper...

Abstract We prove a very general fixed point theorem in the space of functions taking values random normed (RN-space). Next, we show several its consequences and, among others, present applications it proving Ulam stability results for inhomogeneous linear functional equation with variables class f mapping vector X into an RN-space. Particular cases are instance equations Cauchy, Jensen, Jordan...

Abstract: We introduce some fuzzy set-valued functional equations, i.e. the generalized Cauchy type (in n variables), the Quadratic type, the Quadratic-Jensen type, the Cubic type and the Cubic-Jensen type fuzzy set-valued functional equations and discuss the Hyers-Ulam-Rassias stability of the above said functional equations. These results can be regarded as an important extension of stability...