The Hermite-Hadamard inequality has been recognized as the most pivotal which grabbed attention of several mathematicians. In recent years, load results have established for this inequality. main theme article is to present generalized via Jensen-Mercer and majorization concept. We establish a type majorized tuples. With aid weighted Mercer?s inequality, we also prove certain idea obtaining pap...

A Voigt function is the convolution of a Gaus-sian and a Cauchy, or Lorentzian, density. The computation of these functions is required in problems arising in a variety of subjects such as nuclear reactors, atmospheric transmittance, and spectroscopy. This letter presents a new series for the approximate computation of Voigt functions. The derivation is accomplished using straightforward Fourie...

In 1940, Ulam [1] gave a talk before the Mathematics Club of the University of Wisconsin in which he discussed a number of unsolved problems. Among these was the following question concerning the stability of homomorphisms. We are given a group G and a metric group G′ with metric ρ(·,·). Given > 0, does there exist a δ > 0 such that if f :G→G′ satisfies ρ( f (xy), f (x) f (y)) < δ for all x, y ...

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.

The fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated by Moslehian et al. Using fixed point method, we prove the Hyers-Ulam stability of the functional equation

Cădariu and Radu applied the fixed point method to the investigation of Cauchy and Jensen functional equations. In this paper, we adopt the idea of Cădariu and Radu to prove the Hyers-Ulam-Rassias stability of a functional equation of the square root spiral, f (√ r2 + 1 ) = f(r)+ tan−1(1/r).