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1
Content available remote Opial and Pólya type inequalities via convexity
Saker S. H., Abdou D. M., Kubiaczyk I.
Fasciculi Mathematici
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2018
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Nr 60
145--159
EN
In this paper, we prove some new dynamic inequalities related to Opial and Pólya type inequalities on a time scale T. We will derive the integral and discrete inequalities of Polya’s type as special cases and also derive several classical integral inequalities of Opial’s type that has been obtained in the literature as special cases. The main results will be proved by using the chain rule, Hölder’s inequality and Jensen’s inequality, Taylor formula on time scales.
2
Content available remote Existence of solutions of the dynamic Cauchy problem in Banach spaces
Cichoń M., Kubiaczyk I., Sikorska-Nowak A., Yantir A.
Demonstratio Mathematica
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2012
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Vol. 45, nr 3
561-573
EN
In this paper we obtain the existence of solutions and Carathéodory type solutions of the dynamic Cauchy problem in Banach spaces for functions defined on time scales (…), where f is continuous or f satisfies Carathéodory conditions and some conditions expressed in terms of measures of noncompactness. The Mönch fixed point theorem is used to prove the main result, which extends these obtained for real valued functions.
3
Content available remote Common of fixed point of multivalued mappings without continuity
Kubiaczyk I., Deshpande B.
Fasciculi Mathematici
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2007
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Nr 37
19-26
EN
In this paper, we prove a common fixed point theorem for single-valued and multivalued mappings on a metric space using the minimal type commutativity condition. We show that continuity of any mapping is not necessary for the existence of a common fixed point.
4
Content available remote Coincidence point for noncompatible multivalued maps satisfying implicit relation
Kubiaczyk I., Deshpande B.
Demonstratio Mathematica
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2006
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Vol. 39, nr 4
855-862
EN
In this paper we prove a common coincidence point theorem for single- valued and multivalued mappings satisfying an implicit relation under the condition of R-weak commutativity on metric spaces.
5
Content available remote Oscillation and asymptotic behavior of second-order nonlinear difference equations
Kubiaczyk I., Saker S. H.
Fasciculi Mathematici
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2004
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Nr 34
39-54
EN
In this paper we will study the oscillatory and asymptotic behavior of solutions of second-order nonlinear difference equation formula where y > 0 is a quotient of odd positive integers.
6
Content available remote The Asymptotic Stability of the Functional-Integral Equation in Banach Spaces
Kubiaczyk I., Roszak M.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2004
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Vol. 44, nr 2
271-277
7
Content available remote Kamenev-type oscillation criteria for hyperbolic delay difference equations
Kubiaczyk I., Saker S. H.
Demonstratio Mathematica
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2003
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Vol. 36, nr 1
113--122
EN
Some new oscillation criteria and discrete Kamenev-type oscillation criteria for hyperbolic nonlinear delay difference equations are obtained.
8
Oscillation of solutions to nonlinear neutral delay differential equations
Saker S. H., Kubiaczyk I.
Journal of Applied Analysis
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2002
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Vol. 8, nr 2
261-278
EN
In this paper we shall consider the nonlinear neutral delay differential equations with variable coefficients. Some new sufficient conditions for oscillation of all solutions are obtained. Our results extend and improve some of the well known results in the literature. Some examples are considered to illustrate our main results. The neutral logistic equation with variable coefficients is considered to give some new sufficient conditions for oscillation of all positive solutions about its positive steady state.
9
Content available remote Oscillation of parabolic delay differential equations
Kubiaczyk I., Saker S. H.
Demonstratio Mathematica
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2002
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Vol. 35, nr 4
791-802
EN
Some new sufficient conditions for oscillation of all solutions of parabolic delay differential equations with several positive and negative coefficients are obtained. Our results extend and improve the well known results in the literature.
10
Content available remote New oscillation ciriteria of first order delay differential equations
Kubiaczyk I., Saker S. H.
Demonstratio Mathematica
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2002
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Vol. 35, nr 2
313-324
EN
In this paper we shall consider the first order delay differential equations with variable coefficients. Some new sufficient conditions for oscillation of all solutions are obtained. Our results based on the analysis of the generalized charachterestic equation. The results partially improve some previously known results in the literature. Some examples are considered to illustrate our main results.
11
Content available remote Oscillation of parabolic delay differential equations with positive and negative coefficients
Kubiaczyk I., Saker S.H.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2002
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[Z] 42(2)
221-236
EN
Some new sufficient conditions for oscillation of the parabolic delay differential equations with positive and negative coefficients are obtained. Our results extend and improve the well known results in the literature.
12
Content available remote On bounded pseudo and weak solutions of a nonlinear differential equation in Banach spaces
Krzyśka S., Kubiaczyk I.
Demonstratio Mathematica
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1999
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Vol. 32, nr 2
323-330
EN
In this paper, we prove an existence theorem for bounded pseudo and weak solution of the differential equation . XI(t) = A(t)x(t) + f(t, X(t)) where f(., X(.) ) is Pettis- integrable for each strongly absolutely continuous function X and f(t,.) is weakly-weakly sequentially continuous. We also assume some condition expressed in terms of De Blasi's measure of weak noncompactness.
13
Content available remote On the existence of weak solutions of the Darboux problem for the hyperbolic partial differential equations in Banach spaces
Kubiaczyk I., Mostafa Ali N.
Fasciculi Mathematici
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1998
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Nr 28
93-99
EN
In this paper we prove an existence theorem for the hyperbolic partial differential equation zx.y = f(x,y,z,zxy), z(x,O)=o, z(O,y)=O for x,y>O, where Zxy means the second mixed derivative in the weak sence. The continuity of the xy function f is replaced by the weak continuity and the compactness condition is expressed in ternls of the measuresa of weak noncompactness. This paper extends some previous results for our equation.
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