## Related Articles

- RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS IN BANACH SPACES AND HENSTOCK-KURZWEIL-PETTIS INTEGRALS. Sikorska-Nowak, A. // Discussiones Mathematicae: Differential Inclusions, Control & Op;2007, Vol. 27 Issue 2, p315
We prove an existence theorem for the equation xâ€² = f(t, xt) x(Ï´) = Ï†(Ï´), where xt(Ï´) = x(t + Ï´), for -r â‰¤ Ï´ < 0, t Ïµ Ia, Ia = [0, a] a Ïµ R+ in a Banach space, using the Henstock-Kurzweil-Pettis integral and its properties. The requirements on the function f...

- Radon-Nikodym derivatives of finitely additive interval measures taking values in a Banach space with basis. Bongiorno, Benedetto; Piazza, Luisa; Musiał, Kazimierz // Acta Mathematica Sinica;Feb2012, Vol. 28 Issue 2, p219
Let X be a Banach space with a Schauder basis { e}, and let Î¦( I) = Î£ eâˆ« f( t) dt be a finitely additive interval measure on the unit interval [0, 1], where the integrals are taken in the sense of Henstock-Kurzweil. Necessary and sufficient conditions are given for Î¦ to be the...

- DIFFERENTIAL INCLUSIONS AND MULTIVALUED INTEGRALS. CICHOŃ, KINGA; CICHOŃ, MIECZYSŁAW; SATCO, BIANCA // Discussiones Mathematicae: Differential Inclusions, Control & Op;2013, Vol. 33 Issue 2, p171
In this paper we consider the nonlocal (nonstandard) Cauchy problem for differential inclusions in Banach spaces x'(t) âˆŠ F(t, x(t)); x(0) = g(x), t âˆŠ [0, T] = I. Investigation over some multivalued integrals allow us to prove the existence of solutions for considered problem. We...

- STRONG CONVERGENCE IN KENSTOCK-KURZWEIL-PETTIS INTEGRATION UNDER AN EXTREME POINT CONDITION. Satco, B. // Real Analysis Exchange;2005/2006, Vol. 31 Issue 1, p179
In the present paper, some Olech and Visintin-type results are obtained in Henstock-Kurzweil-Pettis integration. More precisely, under extreme or denting point condition, one can pass from weak convergence (i.e. convergence with respect to the topology induced by the tensor product of the space...

- FREDHOLM TYPE INTEGRODIFFERENTIAL EQUATION ON TIME SCALES. PACHPATTE, DEEPAK B. // Electronic Journal of Differential Equations;2010, Vol. 2010, Special section p1
The aim of this article is to study some basic qualitative properties of solutions to Fredholm type integrodifferential equations on time scales. A new integral inequality with explicit estimate on time scales is obtained and used to establish the results.

- SOME DYNAMIC INEQUALITIES APPLICABLE TO PARTIAL INTEGRODIFFERENTIAL EQUATIONS ON TIME SCALES. PACHPATTE, DEEPAK B. // Archivum Mathematicum;2015, Vol. 51 Issue 3, p143
The main objective of the paper is to study explicit bounds of certain dynamic integral inequalities on time scales. Using these inequalities we prove the uniqueness of some partial integrodifferential equations on time scales.

- Extremal Solutions of Periodic Boundary Value Problems for First-Order Impulsive Integrodifferential Equations of Mixed-Type on Time Scales. Yongkun Li; Hongtao Zhang // Boundary Value Problems;2007, p1
We consider the existence of minimal and maximal solutions of periodic boundary value problems for first-order impulsive integrodifferential equations of mixed-type on time scales by establishing a comparison result and using the monotone iterative technique.

- Weak solvability of a hyperbolic integro-differential equation with integral condition. Guezane-Lakoud, A.; Belakroum, D. // Electronic Journal of Qualitative Theory of Differential Equatio;2011, p1
By using the method of semidiscretization in time also called the Rothe's method, we prove the existence, uniqueness of the weak solution and its continuous dependence upon data, for a hyperbolic integrodifferential equation with initial, Neumann and integral conditions.

- Integrable equations on time scales. Gürses, Metin; Guseinov, Gusein Sh.; Silindir, Burcu // Journal of Mathematical Physics;Nov2005, Vol. 46 Issue 11, p113510
Integrable systems are usually given in terms of functions of continuous variables (on R), in terms of functions of discrete variables (on Z), and recently in terms of functions of q-variables (on Kq). We formulate the Gelâ€™fand-Dikii (GD) formalism on time scales by using the delta...

- Fractional Differences and Integration by Parts. Abdeljawad, Thabet; Baleanu, Dumitru // Journal of Computational Analysis & Applications;Apr2011, Vol. 13 Issue 3, p574
In this paper we define the right fractional sum and difference following the delta time scale calculus and obtain results on them analogous to those obtained for the left ones studied in [6], [7], [8]. In addition of that a formula for the integration by parts was obtained. The obtained formula...