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Hammerstein equations with an integral over a noncompact domain

Robert Stańczy (1998)

Annales Polonici Mathematici

The existence of solutions of Hammerstein equations in the space of bounded and continuous functions is proved. It is obtained by the Schauder fixed point theorem using a compactness theorem. The result is applied to Wiener-Hopf equations and to ODE's.

Hammerstein–Nemytskii Type Nonlinear Integral Equations on Half-line in Space L 1 ( 0 , + ) L ( 0 , + )

Aghavard Kh. Khachatryan, Khachatur A. Khachatryan (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The paper studies a construction of nontrivial solution for a class of Hammerstein–Nemytskii type nonlinear integral equations on half-line with noncompact Hammerstein integral operator, which belongs to space L 1 ( 0 , + ) L ( 0 , + ) . This class of equations is the natural generalization of Wiener-Hopf type conservative integral equations. Examples are given to illustrate the results. For one type of considering equations continuity and uniqueness of the solution is established.

Hardy-Rogers-type fixed point theorems for α - G F -contractions

Muhammad Arshad, Eskandar Ameer, Aftab Hussain (2015)

Archivum Mathematicum

The aim of this paper is to introduce some new fixed point results of Hardy-Rogers-type for α - η - G F -contraction in a complete metric space. We extend the concept of F -contraction into an α - η - G F -contraction of Hardy-Rogers-type. An example has been constructed to demonstrate the novelty of our results.

Hybrid fixed point theory for right monotone increasing multi-valued mappings and neutral functional differential inclusions

Bapurao Chandra Dhage (2007)

Archivum Mathematicum

In this paper, some hybrid fixed point theorems for the right monotone increasing multi-valued mappings in ordered Banach spaces are proved via measure of noncompactness and they are further applied to the neutral functional nonconvex differential inclusions involving discontinuous multi-functions for proving the existence results under mixed Lipschitz, compactness and right monotonicity conditions. Our results improve the multi-valued hybrid fixed point theorems of Dhage (Dhage, B. C., A fixed...

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