Let q > 1 and E be a real q−uniformly smooth Banach space. Let K be a nonempty closed convex subset of E and T : K → K be a strictly pseudocontractive mapping in the sense of F. E. Browder and W. V. Petryshyn [1]. Let {un} be a bounded sequence in K and {αn}, {βn}, {γn} be real sequences in [0,1] satisfying some restrictions. Let {xn} be the bounded sequence in K generated from any given x1 ∈ K...

in which the second derivative may occur nonlinearly. Positive solutions for the case f (t,u,u′,u′′) = g(t)h(u) have been studied by Ma [15] and Webb [20, 21], when f (t,u,u′,u′′) = h(t,u) by He and Ge [5] and also by Lan [11]. The case f (t,u,u′,u′′) = g(t)h(u,u′) has been studied by Feng [4]. The results in [4, 15] are obtained by means of Krasnosel’skiı̆’s theorem [8], the ones in [5] use Leg...

Let X and F be real Banach spaces, G a bounded open subset of X, cl(G) its closure in X, bdry(G) its boundary in X. We consider mappings T, (nonlinear, in general), of cl(G) into Y which are A-proper, in the sense defined below, with respect to a given approximation scheme of generalized Galerkin type. We define a generalized concept of topological degree for such mappings with respect to the g...

Let X, d be a metric space and S a closed and nonempty subset of X. Denote by 2 resp., C X the family of all nonempty resp., nonempty and closed subsets of X. A mapping T : S → 2 is said to satisfy condition P if, for every closed ball B of S with radius r ≥ 0 and any sequence {xn} in S for which d xn, B → 0 and d xn, T xn → 0 as n → ∞, there exists x0 ∈ B such that x0 ∈ T x0 where d x, B inf{d...

Our concern is with the Lipschitz constant of T; i.e. with the constant K such that || J # — 7 j | | ^i£||#—;y|| for all x, y in X. In particular, we wish to determine under what conditions on the space X the mapping T will be nonexpansive, i.e. K = l. T is a special case of a proximity mapping defined by a convex set in a normed vector space, i.e. a mapping which assigns to each point of X, th...

1. M. Arkowitz and C. Curjel, The group of homotopy équivalences of a space, Bull. Amer. Math. Soc. 70 (1964), 293-296. 2. Sze-tsen Hu, Homotopy theory. Academic Press, New York, 1959. 3. L. K. Hua and I. Reiner, On the generators of the symplectic modular group, Trans. Amer. Math. Soc. 65 (1949), 415-426. 4. P. J. Kahn, Characteristic numbers and oriented homotopy type, Topology 3 (1965), 81-9...

In this paper, we study the existence of solutions of some nonlinear Volterra integral equations by using the techniques of measures of noncompactness and the Petryshyn's fixed point theorem in Banach space. We also present some examples of the integral equation to confirm the efficiency of our results.

and Applied Analysis 3 It is clear that 1.7 is equivalent to 〈 Sx − Sy, x − y ≤ ∥x − y∥2, ∀x, y ∈ C. 1.8 The class of κ-strict pseudocontractions which was introduced by Browder and Petryshyn 17 in 1967 has been considered by many authors. It is easy to see that the class of strict pseudocontractions falls into the one between the class of nonexpansive mappings and the class of pseudocontractio...