Volume 39, Issue 1

This paper deals with asymptotic behavior of nonoscillatory solutions of certain third-order forced dynamic equations on time scales. The main goal is to investigate when all solutions behave at infinity like certain nontrivial nonlinear functions.

In this paper we study the concept of generalized geometric difference of six-dimensional rough almost lacunary statistical Cesáro of χ3{\chi^{3}} over probabilistic space P is defined by Musielak–Orlicz function. Since the study of convergence in Probabilistic space P is fundamental to probabilistic functional analysis, we feel that the concept of generalized geometric difference of six-dimensional rough almost lacunary statistical Cesáro of χ3{\chi^{3}} over probabilistic space P defined by Musielak in a probabilistic space P would provide a more general framework for the subject.

Given an ideal ℐ{\mathcal{I}} on ω, we prove that a sequence in a topological space X is ℐ{\mathcal{I}}-convergent if and only if there exists a “big” ℐ{\mathcal{I}}-convergent subsequence. Then we study several properties and show two characterizations of the set of ℐ{\mathcal{I}}-cluster points as classical cluster points of a filter on X and as the smallest closed set containing “almost all” the sequence. As a consequence, we obtain that the underlying topology τ coincides with the topology generated by the pair (τ,ℐ){(\tau,\mathcal{I})}.

An asymptotic expansion is constructed for values near the origin of a function whose Kontorovich–Lebedev transform is an even analytic function. The expansion obtained is expressed in terms of the poles and residues of the analytic function and provides an alternative to one obtained by Wong (1981) which becomes inapplicable.