Some Nonlinear Alternatives in Banach Algebras with Applications II

Some Nonlinear Alternatives in Banach Algebras with Applications II

In this paper a nonlinear alternative of Leray-Schauder type is proved in a Banach algebra involving three operators and it is further applied to a functional nonlinear integral equation of mixed type $$x(t)=k(t,x({\mu}(t)))+[f(t,x({\theta}(t)))]\(q(t)+{\int}_0{^{\sigma}^{(t)}}v(t,s)g(s,x({\eta}\(s)))ds\)$$ for proving the existence results in Banach algebras under generalized Lipschitz and $Carath{\acute{e}}odory$ conditions.

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