Applications of some new Krasnoselskii-type fixed-point results for generalized expansive and equiexpansive mappings

Abstract

AbstractWe consider Ω as a subset of a Banach space W and Λ as a function of Ω into W. Let Ϝ be a function whose image values lie in W and domain is $\Lambda (\Omega )\times \Omega $ Λ ( Ω ) × Ω or $\Omega \times \Omega $ Ω × Ω . In this paper, we establish some fixed-point results for a generalized expansive and equiexpansive operator Ϝ such that $\Omega \subseteq \digamma (\Lambda \omega ,\Omega )$ Ω ⊆ Ϝ ( Λ ω , Ω ) or $\Omega \subseteq \digamma (\omega ,\Omega )$ Ω ⊆ Ϝ ( ω , Ω ) . We apply our results to acquire the solutions of fractional evolution equations and certain types of integral equations. We demonstrate our results with examples, and plot approximate and exact solutions with errors.