scholarly journals Novel Investigation of Multivariable Conformable Calculus for Modeling Scientific Phenomena

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Mohammed K. A. Kaabar ◽  
Francisco Martínez ◽  
Inmaculada Martínez ◽  
Zailan Siri ◽  
Silvestre Paredes
Keyword(s):  
Thermohaline Circulation ◽  
Physical Oceanography ◽  
Implicit Function ◽  
Computational Tool ◽  
Conformable Derivative ◽  
Several Variables ◽  
Multivariable Calculus ◽  
Scientific Phenomena ◽  
Vector Valued Functions ◽  
Vector Valued

New investigation on the conformable version (CoV) of multivariable calculus is proposed. The conformable derivative (CoD) of a real-valued function (RVF) of several variables (SVs) and all related properties are investigated. An extension to vector-valued functions (VVFs) of several real variables (SRVs) is studied in this work. The CoV of chain rule (CR) for functions of SVs is also introduced. At the end, the CoV of implicit function theorem (IFThm) for SVs is established. All results in this work can be potentially applied in studying various modeling scenarios in physical oceanography such as Stommel’s box model of thermohaline circulation and other related models where all our results can provide a new analysis and computational tool to investigate these models or their modified formulations.

scholarly journals Vector-Valued Entire Functions of Several Variables: Some Local Properties

Axioms ◽  
2022 ◽  
Vol 11 (1) ◽  
pp. 31
Author(s):  
Andriy Ivanovych Bandura ◽  
Tetyana Mykhailivna Salo ◽  
Oleh Bohdanovych Skaskiv
Keyword(s):  
Continuous Function ◽  
Partial Derivative ◽  
Entire Functions ◽  
Positive Continuous Function ◽  
Several Variables ◽  
Local Properties ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Entire Vector

The present paper is devoted to the properties of entire vector-valued functions of bounded L-index in join variables, where L:Cn→R+n is a positive continuous function. For vector-valued functions from this class we prove some propositions describing their local properties. In particular, these functions possess the property that maximum of norm for some partial derivative at a skeleton of polydisc does not exceed norm of the derivative at the center of polydisc multiplied by some constant. The converse proposition is also true if the described inequality is satisfied for derivative in each variable.

scholarly journals Multi-variable conformable fractional calculus

Filomat ◽  
2018 ◽  
Vol 32 (1) ◽  
pp. 45-53 ◽  
Author(s):  
Nazlı Gözütok ◽  
Uğur Gözütok
Keyword(s):  
Fractional Calculus ◽  
Fractional Derivative ◽  
Conformable Fractional Derivative ◽  
Conformable Derivative ◽  
Several Variables ◽  
Vector Valued Function ◽  
Vector Valued

Conformable fractional derivative is introduced by the authors Khalil et al. In this study we develop their concept and introduce multi-variable conformable derivative for a vector valued function with several variables

scholarly journals Farkas-Type Results for Vector-Valued Functions with Applications

2017 ◽  
Vol 173 (2) ◽  
pp. 357-390 ◽  
Author(s):  
N. Dinh ◽  
M. A. Goberna ◽  
M. A. López ◽  
T. H. Mo
Keyword(s):  
Vector Valued Functions ◽  
Vector Valued

scholarly journals Diameter-preserving linear bijections of function spaces

2001 ◽  
Vol 70 (3) ◽  
pp. 323-336 ◽  
Author(s):  
T. S. S. R. K. Rao ◽  
A. K. Roy
Keyword(s):  
Maximal Ideal ◽  
Convex Set ◽  
Compact Convex ◽  
Extreme Points ◽  
Continuous Functions ◽  
Ideal Space ◽  
Function Algebras ◽  
Compact Convex Set ◽  
Vector Valued Functions ◽  
Vector Valued

AbstractIn this paper we give a complete description of diameter-preserving linear bijections on the space of affine continuous functions on a compact convex set whose extreme points are split faces. We also give a description of such maps on function algebras considered on their maximal ideal space. We formulate and prove similar results for spaces of vector-valued functions.

scholarly journals THE LOCAL NON-HOMOGENEOUS Tb THEOREM FOR VECTOR-VALUED FUNCTIONS

2014 ◽  
Vol 57 (1) ◽  
pp. 17-82 ◽  
Author(s):  
TUOMAS P. HYTÖNEN ◽  
ANTTI V. VÄHÄKANGAS
Keyword(s):  
Singular Integrals ◽  
Local Version ◽  
Square Functions ◽  
Property A ◽  
Martingale Differences ◽  
Umd Spaces ◽  
Function Lattice ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Similar Extension

AbstractWe extend the local non-homogeneous Tb theorem of Nazarov, Treil and Volberg to the setting of singular integrals with operator-valued kernel that act on vector-valued functions. Here, ‘vector-valued’ means ‘taking values in a function lattice with the UMD (unconditional martingale differences) property’. A similar extension (but for general UMD spaces rather than UMD lattices) of Nazarov-Treil-Volberg's global non-homogeneous Tb theorem was achieved earlier by the first author, and it has found applications in the work of Mayboroda and Volberg on square-functions and rectifiability. Our local version requires several elaborations of the previous techniques, and raises new questions about the limits of the vector-valued theory.

Strict Topologies for Vector-Valued Functions

1974 ◽  
Vol 26 (4) ◽  
pp. 841-853 ◽  
Author(s):  
Robert A. Fontenot
Keyword(s):  
Vector Space ◽  
Topological Vector Space ◽  
Measure Theory ◽  
Strict Topology ◽  
Locally Compact ◽  
Topological Measure ◽  
Topological Measure Theory ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Locally Compact Hausdorff Space

This paper is motivated by work in two fields, the theory of strict topologies and topological measure theory. In [1], R. C. Buck began the study of the strict topology for the algebra C*(S) of continuous, bounded real-valued functions on a locally compact Hausdorff space S and showed that the topological vector space C*(S) with the strict topology has many of the same topological vector space properties as C0(S), the sup norm algebra of continuous realvalued functions vanishing at infinity. Buck showed that as a class, the algebras C*(S) for S locally compact and C*(X), for X compact, were very much alike. Many papers on the strict topology for C*(S), where S is locally compact, followed Buck's; e.g., see [2; 3].

scholarly journals Refined limiting imbeddings for Sobolev spaces of vector-valued functions

2005 ◽  
Vol 227 (2) ◽  
pp. 372-388 ◽  
Author(s):  
Miroslav Krbec ◽  
Hans-Jürgen Schmeisser
Keyword(s):  
Sobolev Spaces ◽  
Vector Valued Functions ◽  
Vector Valued
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