Authors:
John T Mendy
Pages: 1 - 8 Abstract: In this paper, we study the viscosity iterative algorithms for the implicit double midpoint rule in real Hilbert space and prove strong convergence of the sequence {un} to a fixed point of T. As an application we employ our method to obtain an application of it in convex minimization and the solution of Fredholm type of integral equations. PubDate: 2020-05-20 DOI: 10.12691/ajma-8-1-1 Issue No:Vol. 8, No. 1 (2020)

Authors:
Suresh Kumar Sahani
Pages: 9 - 13 Abstract: This paper briefly discusses the uniform (N, p, q) summability of Fourier series and its conjugate series. We prove that if and be positive (i.e. monotric function of t) and and is monotonic sequence of constant with their non-vanishing partial sums and tending to infinity as m, n if = 0 as n 0 as n Where 0 and as t uniformly in a domain E in which f(x) is bounded then the Fourier series (1.4) is summable (N, p, q) uniformly in E to the sum f(x). Also, If (2.4) uniformly in E then (1.5) is summable (N, p,q) uniformly in the domain E to the sum (2.5) whenever the integral exist uniformly in E. PubDate: 2020-06-15 DOI: 10.12691/ajma-8-1-2 Issue No:Vol. 8, No. 1 (2020)

Authors:
Michael Parfenov
Pages: 14 - 30 Abstract: The so-called essentially adequate concept of quaternionic holomorphic ( -holomorphic) functions defined as functions, whose quaternionic derivatives are independent of "the way of their computation", is developed. It is established that -holomorphic functions form one remarkable class of quaternionic functions whose properties are fully similar (essentially adequate) to complex ones: the quaternionic multiplication of these quaternionic functions behaves as commutative, the left quotient equals the right one, the rules for differentiating sums, products, ratios, inverses, and compositions are the same as in complex analysis. One can just verify these properties, constructing -holomorphic functions from their complex holomorphic counterparts by using the presented constructing rule. Several examples, confirming the theory in question, are considered. When using this concept there are no principal restrictions to build a quaternionic analysis similar to complex one. The elementary source flow and elementary vortex flow, allowing us to construct different 3D steady state fluid flows by superposition, are considered. To automate the processing of -holomorphic functions the pack of Mathematica® Programs is developed, part of which is presented. PubDate: 2020-07-05 DOI: 10.12691/ajma-8-1-3 Issue No:Vol. 8, No. 1 (2020)