Turkish Journal of Analysis and Number Theory

3

Authors: Mohd. Farman Ali, Manoj Sharma, Lakshmi Narayan Mishra, Vishnu N. Mishra

The object of the present paper is to establish the results of single Dirichlet average of Generalized Miller-Ross Function, using Riemann-Liouville Fractional Integral. The Generalized Miller-Ross Function can be measured as a Dirichlet average and connected with fractional calculus. In this paper the solution comes in compact form of single Dirichlet average of Generalized Miller-Ross Function. The special cases of our results are same as earlier obtained by Saxena et al. [12], for single Dirichlet average of Generalized Miller-Ross Function.

4

Authors: O. Yaremko, N. Yaremko, T. Eliseeva

The solution of Hamburger and Stieltjes moment problem can be thought of as the solution of a certain inverse Cauchy problem. The solution of the inverse Cauchy problem for heat equation is founded in the form of Hermite polynomial series. The author reveals, the formulas obtained by him for the solution of inverse Cauchy problem have a symmetry with respect to the formulas for corresponding direct Cauchy problem. Obtained formulas for solution of the inverse problems can serve as a basis for the solution of the moment problem.

5

Authors: Shaad P. Sufi

The purpose of this paper is to introduce a new pattern in Primes numbers, to eliminate the randomness in their patterns. This paper also justifies the solutions in a numerical and geometric manner. The Prime Function provides further distinction in the nature of Prime Numbers by distinguishing the nature of normality and Abnormality in Prime Numbers. To verify the normality of corresponding Prime numbers, the Sufi primality test is formed. Also using the Prime Function, the formula for the approximate sum of Prime Numbers is derived. The limitations and conditions of the Prime function are also stated. These factors provide a panoramic view of the Prime Function and its potential factor in Number Theory .

6

Authors: Kastriot Zoto, Arben Isufati, Panda Sumati Kumari

We prove several fixed points theorems for weakly compatible selfmappings on a dislocated and dislocated quasi-metric space, which satisfy E. A Like and common E. A. Like property, satisfying liner type of contractive condition.