On the solvability of nonlinear operator equations in normed spaces

Generalized coincidence theory for set-valued maps

“…In particular we present continuation theorems and generalized topological transversality theorems. We will also discuss Φ-epi maps [5,13] in this paper.…”

Strong Surjections and Nearness

“…Also, these concepts are related to that of zero-epi map, which is due to the same authors [4] and is very important in the study of solvability of nonlinear equations. Near operators have been introduced by S. Campanato and also studied by A. Tarsia and S. Leonardi in [2,7,10,13,14] and have applications in nonlinear differential equations, too.…”

“…M. Furi, M. Martelli and A. Vignoli in [3] introduced the notions of strong surjection and stable solvable map between two normed spaces E and F in order to define the spectrum for a nonlinear operator. Also, these concepts are related to that of zero-epi map, which is due to the same authors [4] and is very important in the study of solvability of nonlinear equations. Near operators have been introduced by S. Campanato and also studied by A. Tarsia and S. Leonardi in [2,7,10,13,14] and have applications in nonlinear differential equations, too.…”

“…Let us consider two mappings L, N : E → F such that L − N is a strong surjection. In applications (see [4,5,8,11]), usually, L is linear and bounded (in many cases, a differential operator) and N is completely continuous . In the case that ||(L − N )(x)|| → ∞ as ||x|| → ∞ there are some relations between the theory of strong surjections and the theory of zero-epi maps, or degree theory, or the theory of essential compact fields (see [3,4,7,9]).…”

Fixed Point Theory of Multivalued Weighted Maps

“…Granas ([49]) and further generalized by L. Górniewicz and M.Ślosarski for some class of multivalued maps ( [46]). Moreover, the above concept was elaborated by M. Furi, M. Martelli and A. Vignoli under the name zero-epi maps ( [39]). …”