‎inspired by the work of suzuki in‎ ‎[t. suzuki‎, ‎a generalized banach contraction principle that characterizes metric completeness‎, proc‎. ‎amer‎. ‎math‎. ‎soc. ‎136 (2008)‎, ‎1861--1869]‎, ‎we prove a fixed point theorem for contractive mappings‎ ‎that generalizes a theorem of geraghty in [m.a‎. ‎geraghty‎, ‎on contractive mappings‎, ‎proc‎. ‎amer‎. ‎math‎. ‎soc., ‎40 (1973)‎, ‎604--608]‎an...

ACKNOWLEDGMENTS This note was inspired by Brian Davies, who challenged Nick Trefethen at Oxford by pointing out that the evaluation of the integral (7) would cause serious difficulties both analytically and numerically. One of the authors (T.S.) had the pleasure of attending Trefethen’s course in Oxford, where problems like Davies’s had to be solved on a weekly basis. Discussing the integral wi...

in this paper, an attempt is made to present an extension of darbo's theorem, and its applicationto study the solvability of a functional integral equation of volterra type.

n this article, we prove an lp-lq-version of morgan’s theorem for the generalized bessel transform.