scholarly journals An Existence Result for Henstock-Kurzweil-Stieltjes-⋄-Double Integral of Interval-Valued Functions on Time Scales

2021 ◽  
Vol 4 (2) ◽  
pp. 1-7
Author(s):  
David Adebisi Afariogun ◽  
Adesanmi Alao Mogbademu
Keyword(s):  
Time Scales ◽  
Existence Result ◽  
Double Integral ◽  
Interval Valued

We employ the concept of interval-valued functions to state and prove an existence result for the Henstock-Kurzweil-Stieltjes-⋄-double integral on time scales.

scholarly journals On Fuzzy Henstock-Kurzweil-Stieltjes-♦-Double Integral on Time scales

2021 ◽  
Vol 2 (2) ◽  
pp. 38-49
Author(s):  
David AFARIOGUN ◽  
Adesanmi MOGBADEMU ◽  
Hallowed OLAOLUWA
Keyword(s):  
Uniform Convergence ◽  
Time Scales ◽  
Convergence Theorem ◽  
Monotone Convergence ◽  
Double Integral ◽  
Monotone Convergence Theorem ◽  
Integrable Functions ◽  
Dominated Convergence

We introduce and study some properties of fuzzy Henstock-Kurzweil-Stietljes-$ \Diamond $-double integral on time scales. Also, we state and prove the uniform convergence theorem, monotone convergence theorem and dominated convergence theorem for the fuzzy Henstock-Kurzweil Stieltjes-$\Diamond$-double integrable functions on time scales.

scholarly journals Some inequalities for interval-valued functions on time scales

2018 ◽  
Vol 23 (15) ◽  
pp. 6005-6015 ◽  
Author(s):  
Dafang Zhao ◽  
Guoju Ye ◽  
Wei Liu ◽  
Delfim F. M. Torres
Keyword(s):  
Time Scales ◽  
Interval Valued

scholarly journals Bounds of Double Integral Dynamic Inequalities in Two Independent Variables on Time Scales

2011 ◽  
Vol 2011 ◽  
pp. 1-21 ◽  
Author(s):  
S. H. Saker
Keyword(s):  
Time Scales ◽  
Unknown Function ◽  
The Other ◽  
Dynamic Equations ◽  
Double Integral ◽  
Independent Variables ◽  
Explicit Bounds ◽  
Quantitative Properties ◽  
The One ◽  
Two Independent Variables

Our aim in this paper is to establish some explicit bounds of the unknown function in a certain class of nonlinear dynamic inequalities in two independent variables on time scales which are unbounded above. These on the one hand generalize and on the other hand furnish a handy tool for the study of qualitative as well as quantitative properties of solutions of partial dynamic equations on time scales. Some examples are considered to demonstrate the applications of the results.

scholarly journals Double integral calculus of variations on time scales

2007 ◽  
Vol 54 (1) ◽  
pp. 45-57 ◽  
Author(s):  
Martin Bohner ◽  
Gusein Sh. Guseinov
Keyword(s):  
Calculus Of Variations ◽  
Time Scales ◽  
Double Integral ◽  
Integral Calculus

scholarly journals Generalized double-integral Ostrowski type inequalities on time scales

2011 ◽  
Vol 24 (8) ◽  
pp. 1461-1467 ◽  
Author(s):  
Sabir Hussain ◽  
Muhammad Amer Latif ◽  
Mohammad Alomari
Keyword(s):  
Time Scales ◽  
Double Integral

scholarly journals Fuzzy integral inequalities on coordinates of convex fuzzy interval-valued functions

2021 ◽  
Vol 18 (5) ◽  
pp. 6552-6580
Author(s):  
Muhammad Bilal Khan ◽  
◽  
Pshtiwan Othman Mohammed ◽  
Muhammad Aslam Noor ◽  
Khadijah M. Abualnaja ◽  
...  
Keyword(s):  
Order Relation ◽  
Strong Relationship ◽  
Double Integral ◽  
New Class ◽  
Fundamental Properties ◽  
Starting Point ◽  
Special Cases ◽  
Fuzzy Order ◽  
Interval Valued ◽  
Fuzzy Interval

<abstract> <p>In this study, we introduce and study new fuzzy-interval integral is known as fuzzy-interval double integral, where the integrand is fuzzy-interval-valued functions (FIVFs). Also, some fundamental properties are also investigated. Moreover, we present a new class of convex fuzzy-interval-valued functions is known as coordinated convex fuzzy-interval-valued functions (coordinated convex FIVFs) through fuzzy order relation (FOR). The FOR $\left(\preccurlyeq \right)$ and fuzzy inclusion relation (⊇) are two different concepts. With the help of fuzzy-interval double integral and FOR, we have proved that coordinated convex fuzzy-IVF establish a strong relationship between Hermite-Hadamard (<italic>HH</italic>-) and Hermite-Hadamard-Fejér (<italic>HH</italic>-Fejér) inequalities. With the support of this relation, we also derive some related <italic>HH</italic>-inequalities for the product of coordinated convex FIVFs. Some special cases are also discussed. Useful examples that verify the applicability of the theory developed in this study are presented. The concepts and techniques of this paper may be a starting point for further research in this area.</p> </abstract>

scholarly journals Solvability of a Higher-Order Three-Point Boundary Value Problem on Time Scales

2009 ◽  
Vol 2009 ◽  
pp. 1-16 ◽  
Author(s):  
Yanbin Sang
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Time Scales ◽  
Existence Result ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Growth Conditions ◽  
Higher Order ◽  
Point Boundary ◽  
Nonlinear Alternative

We consider a higher-order three-point boundary value problem on time scales. A new existence result is first obtained by using a fixed point theorem due to Krasnoselskii and Zabreiko. Later, under certain growth conditions imposed on the nonlinearity, several sufficient conditions for the existence of a nonnegative and nontrivial solution are obtained by using Leray-Schauder nonlinear alternative. Our conditions imposed on nonlinearity are all very easy to verify; as an application, some examples to demonstrate our results are given.

scholarly journals On Gronwall type inequalities for interval-valued functions on time scales

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Awais Younus ◽  
Muhammad Asif ◽  
Khurram Farhad
Keyword(s):  
Time Scales ◽  
Interval Valued

Henstock-Kurzweil-Pettis integral and weak topologies in nonlinear integral equations on time scales

2013 ◽  
Vol 63 (6) ◽  
Author(s):  
Bianca-Renata Satco ◽  
Corneliu-Octavian Turcu
Keyword(s):  
Integral Equation ◽  
Time Scales ◽  
Existence Result ◽  
Nonlinear Integral Equation ◽  
Continuity Condition ◽  
Pettis Integral ◽  
Nonlinear Integral Equations ◽  
Weakly Continuous ◽  
The Right ◽  
Weak Topologies

AbstractThe goal of the present work is to give an existence result for a nonlinear integral equation on time scales by considering the Banach space endowed with its weak topology. More precisely, we obtain the existence of weakly continuous solutions for an integral equation that has on the right hand side the sum of two operators, one of them continuous while the other one satisfies a partial continuity condition and some integrability (in a nonabsolute sense) assumptions.

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