A Baire function not countably decomposable into continuous functions
A category analogue of the density topology
A class of subadditively continuous real functions
A companion of Ostrowski's inequality for mappings whose first derivatives are bounded and applications in numerical integration
A family of singular functions and its relation to harmonic fractal analysis and fuzzy logic
We study a parameterized family of singular functions which appears in a paper by H. Okamoto and M. Wunsch (2007). Various properties are revisited from the viewpoint of fractal geometry and probabilistic techniques. Hausdorff dimensions are calculated for several sets related to these functions, and new properties close to fractal analysis and strong negations are explored.
A hierarchy in the family of real surjective functions
This expository paper focuses on the study of extreme surjective functions in ℝℝ. We present several different types of extreme surjectivity by providing examples and crucial properties. These examples help us to establish a hierarchy within the different classes of surjectivity we deal with. The classes presented here are: everywhere surjective functions, strongly everywhere surjective functions, κ-everywhere surjective functions, perfectly everywhere surjective functions and Jones functions. The...
A Marchaud type inequality
We present a new Marchaud type inequality in spaces.
A mean value property for pairs of integrals.
A necessary and sufficient condition for continuity of additive functions
A new extension of monotone sequences and its applications.
A nonlinear Banach-Steinhaus theorem and some meager sets in Banach spaces
We establish a Banach-Steinhaus type theorem for nonlinear functionals of several variables. As an application, we obtain extensions of the recent results of Balcerzak and Wachowicz on some meager subsets of L¹(μ) × L¹(μ) and c₀ × c₀. As another consequence, we get a Banach-Mazurkiewicz type theorem on some residual subset of C[0,1] involving Kharazishvili's notion of Φ-derivative.
A nonstandard analysis characterization of Arzela's quasi-uniform convergence for sequences of real functions
A note about the almost continuity
A note on almost contra-precontinuous functions.
A Note on Discontinuous Functions.
A note on separate continuity and connectivity properties
Separately continuous functions are shown to have certain properties related to connectedness.
A note on separation of sets by approximately continuous functions
A note on symmetrically continuous functions
A Sierpiński-Zygmund function which has a perfect road at each point
About the Maximum and the Minimum of Darboux Functions