... economy. See 6 for a nicesurvey.2. Notations and Basic ConceptsThroughout this paper, the standard notations and terminologies in nonlinear analysis areused see the papers by Kirk and Sims 7, ... 36. For some problems for other classes of generalized contractions, see for example, 17, 21, 27, 34, 37.AcknowledgmentsThe second and the forth authors wish to thank National Council of Research ... Dshalalow, and D. O’Regan, “Fixed point and homotopy results for generalizedcontractive maps of Reich type,” Applicable Analysis, vol. 82, no. 4, pp. 329–350, 2003.18 J. Andres and L. G´orniewicz,...