The best proximity point is a generalization of a fixed point that is beneficial when the contraction map is not a self-map. On other hand, best approximation theorems offer an approximate solution to the fixed point equation . It is used to solve the problem in order to come up with a good approximation. This paper's main purpose is to introduce new types of proximal contraction for nonself mappings in fuzzy normed space and then proved the best proximity point theorem for these mappings. At first, the definition of fuzzy normed space is given. Then the notions of the best proximity point and - proximal admissible in the context of fuzzy normed space are presented. The notion of α ̃–ψ ̃- proximal contractive mapping is introduced.

The appearance of Mixed Mode Oscillations (MMOs) and chaotic spiking in a Light Emitting Diode (LED) with optoelectronic feedback theoretically and experimentally have been reported. The transition between periodic and chaotic mixed-mode states has been investigated by varying feedback strength. In incoherent semiconductor chaotically spiking attractors with optoelectronic feedback have been observed to be the result of canard phenomena in three-dimensional phase space (incomplete homoclinic scenarios).

By use the notions pre-g-closedness and pre-g-openness we have generalized a class of separation axioms in topological spaces. In particular, we presented in this paper new types of regulαrities, which we named ρg­regulαrity and Sρg­regulαrity. Many results and properties of both types have been investigated and have illustrated by examples.

In this work the concept of semi-generalized regular topological space was introduced and studied via semi generalized open sets. Many properties and results was investigated and studied, also it was shown that the quotient space of semi-generalized regular topological space is not, in general semi-generalizedspace.

One of the most important problems in the statistical inference is estimating parameters and Reliability parameter and also interval estimation , and testing hypothesis . estimating two parameters of exponential distribution and also reliability parameter in a stress-strength model.

This parameter deals with estimating the scale parameter and the Location parameter µ , of two exponential distribution   ,using moments estimator and maximum likelihood estimator , also we estimate the parameter R=pr(x>y), where x,y are two- parameter independent exponential random variables .

Statistical properties of this distribution and its properti