Using the concept of Orlicz function and uncertainty theory, some new class lacunary convergent sequences defined by functions have been introduced with convergence concepts in this paper. Some topological properties sequence spaces along inclusion relations investigated.

In the present paper we find optimal conditions separating regular case from one with Lavrentiev gap for borderline of double phase potential saddle point and related general classes integrands.

Let f be a function in an Orlicz space L and μ(f,L) be the set of all the best Φ-approximants to f, given a σ−lattice L. Weak type inequalities are proved for the maximal operator f∗ = supn |fn|, where fn is any selection of functions in μ(f,Ln), and Ln is an increasing sequence of σ-lattices. Strong inequalities are proved in an abstract set up which can be used for an operator as f∗.

In this paper, the extended Musielak-Orlicz-Gauss image problem is studied. Such a aims to characterize measure $\widetilde{C}_{G,\Psi,\lambda}(\Omega,\cdot)$ of convex body $\Omega$ in $\mathbb{R}^{n+1}$ containing origin (but not necessary its interior). particular, we provide solutions based on study suitably designed parabolic flows, and by use approximation technique (for general measures)...

Abstract We study the existence of a.e. monotonic $$L_\varphi $$ L φ -solutions for product n -quadratic integral equations. As indicated by different continuity properties considered operators in Orlicz spaces, we three cases which generating N -functions satisfy condi...