Integrable solutions of Hammerstein and Urysohn integral equations

Banaś, Józef

doi:10.1017/s1446788700030378

Cited by 71 publications

(31 citation statements)

References 6 publications

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“…nonincreasing on I. Similarly as claimed in [10] we are able to show that this set is nonempty, bounded (by R), convex and closed in L 1 (I). Only the last property needs some comments.…”

Section: Theorem 31 Let the Assumptions (I)-(vi) Be Satisfied Putsupporting

confidence: 82%

On Monotonic Integrable Solutions for Quadratic Functional Integral Equations

Cichoń

Metwali

2012

Mediterr. J. Math.

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Abstract. We study the solvability of functional quadratic integral equations in the space of integrable functions on the interval I = [0, 1]. We concentrate on a.e. monotonic solutions for considered problems. The existence result is obtained under the assumption that the functions involved in the investigated equation satisfy Carathéodory conditions. As a solution space we consider both L1(I) and Lp(I) spaces for p > 1. Mathematics Subject Classification (2010). Primary 45G10; Secondary 47H30, 47N20.

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“…nonincreasing on I. Similarly as claimed in [10] we are able to show that this set is nonempty, bounded (by R), convex and closed in L 1 (I). Only the last property needs some comments.…”

Section: Theorem 31 Let the Assumptions (I)-(vi) Be Satisfied Putsupporting

confidence: 82%

On Monotonic Integrable Solutions for Quadratic Functional Integral Equations

Cichoń

Metwali

2012

Mediterr. J. Math.

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“…This observation is well known (cf. [8] or [27]). Surprisingly, to the best of our knowledge, there is no published proof, even for sets of continuous functions.…”

Section: Vol 18 (2016) On a Fixed Point Theorem 763mentioning

confidence: 99%

“…Note that this is a weak version of Helly's selection theorem (cf. [8,16] Proof. Let us recall that a topology of convergence in measure is a metric topology (cf.…”

Section: Vol 18 (2016) On a Fixed Point Theorem 763mentioning

confidence: 99%

On a fixed point theorem for the product of operators

Cichoń

Metwali

2016

J. Fixed Point Theory Appl.

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Abstract. In this paper, we study the existence of fixed points for the product of nonlinear operators. This kind of fixed point theorems is necessary in consideration of quadratic differential and integral problems. We emphasize a possible extension of the applicability of obtained theorems and consequently we prove the existence of fixed points for operators acting on some function spaces that are not necessarily Banach algebras. This result can be successfully applied to many quadratic problems.Mathematics Subject Classification. 46E30, 45G10, 47H30, 47N20.

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“…: WIE -> [0,oo) defined in the following way: [2] Let us observe that in the case when E is a reflexive Banach space then 0(X) -0 for every X £ SJtjs. Hence it is only of interest to consider the function /?…”

Section: Notation and Definitionsmentioning

confidence: 99%

“…This measure was applied successfully to nonlinear functional analysis, to operator theory and to the theory of differential and integral equations (see [1,2,3,5,7,8], for example).…”

Section: Introductionmentioning

confidence: 99%