... asymptotically nonexpansive in the intermediatesense, then T has a fixed point. It is worth mentioning that the class of mappings whichare asymptotically nonexpansive in the intermediate sense contains ... compact assumption.14 Fixed Point Theory and Applications4 F. E. Browder and W. V. Petryshyn, “Construction of fixed points of nonlinear mappings in Hilbertspace,” Journal of Mathematical ... νn.1.23Letting n → in 1.23,weobtainthatTnf → f. Since T is uniformly L-Lipschitz, we seethat f Tf. This completes the proof of the convexity of FT. From the continuity of T,wecan also obtain...