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In this article we develop the concepts of $\sigma$-relation and $\sigma$-function, following the same steps as in Set Theory. First we define the concept of ordered pair and then we build the Cartesian Product of $\sigma$-sets so that we…
The present article is devoted to the generalized Salem functions, the generailed shift operator, and certain related problems. A description of further investigations of the author of this article is given.These investigations (in terms of…
We present a general fixed point theorem which can be seen as the quintessence of the principles of proof for Banach's Fixed Point Theorem, ultrametric and certain topological fixed point theorems. It works in a minimal setting, not…
In this article, we discuss a new version of metric fixed point theory especially of Banach Contraction Principle, Ran-Reurings Theorem and others.
In this paper we study the existence and uniqueness of fixed points of a class of mappings defined on complete, (sequentially compact) cone metric spaces, without continuity conditions and depending on another function.
A new classification of real functions and other related real objects defined within a compact interval is proposed. The scope of the classification includes normal real functions and distributions in the sense of Schwartz, referred to…
The present article is an extended version of [6] containing new results and an updated list of references. We review the notion of polar analyticity introduced in a previous paper and succesfully applied in Mellin analysis and quadrature…
We work with semi-algebraic functions on arbitrary real closed fields. We generalize the notion of critical values and prove a Sard type theorem in our framework.
Having a function $f$ and a set of functionals $\{\mathcal{C}_{n}\}$, $c_n^f \equiv \mathcal{C}_n \left(f\right)$, one can interpret function approximation very generally as a construction of some function $\mathcal{A}_{N}^{f}$ such that…
We establish common fixed point theorems for two pairs of weakly compatible self-mappings using an auxiliary function of two variables. Unlike classical results, our theorems do not assume continuity of the mappings and require completeness…
In this paper, we consider a wider class of simulation functions and present some coincidence and common fixed point results in metric spaces. Results obtained in this paper extend, generalize and unify some well-known fixed and common…
An elementary general result is proved that allows for simple characterizations of well-known location/consensus functions (median, mean and center) on the n-cube. In addition, alternate new characterizations are given for the median and…
In this article we discuss the solvability of some class of fully nonlinear equations, and equations with p-Laplacian in more general conditions by using a new approach given in [1] for studying the nonlinear continuous operator. Moreover…
We introduce the notion of Dunkl completely monotonic functions on $\left(-\sigma,\sigma\right), \sigma>0$. We establish a restrictive version of the analogue of Schoenberg's theorem in Dunkl setting.
In this paper we prove a version of the Fountain Theorem for a class of nonsmooth functionals that are sum of a $C^1$ functional and a convex lower semicontinuous functional, and also a version of a theorem due to Heinz for this class of…
We first exhibit counterexamples to some open questions related to a theorem of Sakai. Then we establish an extension theorem of Sakai type for separately holomorphic/meromorphic functions.
In this paper, we generalize the Gauduchon metrics on a compact complex manifold and define the $\gamma_k$ functions on the space of its hermitian metrics.
We simplify the proof of some widely used theoretical theorems, extending their applicability, while correcting some erroneous results. We also generalize key results and present new results that contribute to the development of the theory.…
We give two proofs of the Kalman Theorem, alternative to the most common ones, which infer such a classical result of Control Theory using just very basic facts on flows of vector fields. These proofs are apt to be generalised in diverse…
We show that it is possible to approximate the zeta-function of a curve over a finite field by meromorphic functions which satisfy the same functional equation and moreover satisfy (respectively do not satisfy) the analogue of the Riemann…