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The work is devoted to the construction of a new type of intervals -- functional intervals. These intervals are built on the idea of expanding boundaries from numbers to functions. Functional intervals have shown themselves to be promising…
This paper proposes a new generalized Seikkala derivative (gS-derivative) of a fuzzy-valued function. We see that, there are many elementary fuzzy-valued functions which occur frequently as solution of fuzzy differential equation, are not…
In this work it is described all normal extensions of a multipoint minimal operator generated by linear multipoint differential-operator expression for second order in the Hilbert space of vector-functions in terms of boundary values at the…
We investigate an extended version of Hilbert space of analytic functions called Hilbert space of complex-valued harmonic functions. It is found that functions in Hilbert space of complex-valued harmonic functions exhibit many properties…
In the literature, the left-side of Hermite--Hadamard's inequality is called a midpoint type inequality. In this article, we obtain new integral inequalities of midpoint type for Riemann--Liouville fractional integrals of convex functions…
The concept of moment differentiation is extended to the class of moment summable functions, giving rise to moment differential properties. The main result leans on accurate upper estimates for the integral representation of the moment…
We show that the monotonic independence introduced by Muraki can also be used to define a multiplicative convolution. We also find a method for the calculation of this convolution based on an appropriate form of the Cauchy transform. We…
Borrowing the idea of topological pressure determining measure-theoretical entropy in topological dynamical systems, we establish a variational principle for upper metric mean dimension with potential in terms of upper measure-theoretical…
This paper is devoted to a systematic study and characterizations of the fundamental notions of variational and strong variational convexity for lower semicontinuous functions. While these notions have been quite recently introduced by…
A higher dimensional modified gravity theory with an action that includes dimensionally continued Euler-Poincar\'e forms up to second order in curvatures is considered. The variational field equations are derived. Matter in the universe at…
We give a commutative valuations monad Z on the category DCPO of dcpo's and Scott-continuous functions. Compared to the commutative valuations monads given in [Jia et al., 2021], our new monad Z is larger and it contains all push-forward…
Let $[a,b]\subset\mathbb{R}$ be a non empty and non singleton closed interval and $P=\{a=x_0<\cdots<x_n=b\}$ is a partition of it. Then $f:I\to\mathbb{R}$ is said to be a function of $r$-bounded variation, if the expression…
We obtain a complete characterization of planar monotone $\sigma$-continuous valuations taking integer values, without assuming invariance under any group of transformations. We further investigate the consequences of dropping monotonicity…
We present an approach for construction of functional bases of differential invariants for some infinite-dimensional algebras with coefficients of generating operators depending on arbitrary functions. An example for the…
The paper proposes a vector generalization of the basic concepts of the theory of complex variable: the concept of modulus and argument of complex number. The author introduces some generalizations of the notion of holomorphic functions and…
The method of separation of variables is significant, it has been applied to physics, engineering , chemistry and other fields. It allows to reduce the diffculity of problems by separating the variables from partial differential equation…
Motivated by applications to stochastic programming, we introduce and study the expected-integral functionals, which are mappings given in an integral form depending on two variables, the first a finite dimensional decision vector and the…
We introduce and study spaces of multivariate functions of bounded variation generalizing the classical Jordan and Wiener spaces. Multivariate generalizations of the Jordan space were given by several prominent researchers but each of them…
We develop a functional model for operators arising in the study of boundary-value problems of materials science and mathematical physics. We then provide explicit formulae for the resolvents of the associated extensions of symmetric…
The connection between multiple modular L-functions, as defined by Manin in [5], and modular iterated integrals was made explicit by Choie and Ihara [3] under the restrictive assumption that all modular forms involved have vanishing…