Completely monotone sequences and harmonic mappings

In the present paper, we will study geometric properties of harmonic mappings whose analytic and co-analytic parts are (shifted) generated functions of completely monotone sequences.

Uniform Convergence of Cosine Series With Coefficient from New Class of General Monotone

General monotone sequences class (GMS) has been introduced by Tikhonov. Then Bogdan Szal extended this class to the new class called new class of general monotone. By using non-negative sequence is called 𝛽 to controle the difference of sine series coefficient. By substituting 𝛽 of modulus of sine series coefficient, we study uniform convergence of new class of general monotone on cosine series.

Method of upper and lower solutions for nonlinear Caputo fractional difference equations and its applications

In this paper, we extend the applications of the method of upper and lower solutions for a class of nonlinear nabla fractional difference equations involving Caputo derivative. We obtain the existence of coupled minimal and maximal solutions which constructed by two monotone sequences. In order to illustrate our main results, we present two numerical examples in the end.