and Applied Analysis 3 Remark 1.1. If E is a reflexive strictly convex and smooth Banach space, then for x, y ∈ E, φ x, y 0 if and only if x y. It is sufficient to show that if φ x, y 0 then x y. From 1.6 , we have ‖x‖ ‖y‖. This implies 〈x, Jy〉 ‖x‖2 ‖Jy‖2. From the definitions of j, we have Jx Jy, that is, x y, see 8, 9 for more details. Let C be a nonempty closed convex subset of a smooth Bana...

It is well-known that a polynomial f(z) = adz(1 + o(1)) can be conjugated by a holomorphic map φ to w 7→ w in a neighbourhood of in nity. This map φ is called a Böttcher coordinate for f near in nity. In this paper we construct a Böttcher type coordinate for compositions of a ne mappings and polynomials, a class of mappings rst studied in [9]. As an application, we prove that if h is a ne and c...

in the present paper‎, ‎we introduce the concept of generalized multivalued $f$ -‎contraction mappings and give a fixed point result‎, ‎which is a proper‎ ‎generalization of some multivalued fixed point theorems including nadler's‎.

Recently, Kawasaki and Takahashi [8] defined a broad class of nonlinear mappings, called widely more generalized hybrid, in a Hilbert space which contains generalized hybrid mappings [9] and strict pseudo-contractive mappings [2]. They proved fixed point theorems for such mappings. In this paper, we prove fixed point theorems for widely more generalized hybrid nonself mappings in a Hilbert spac...

We introduce the notion of quasi-cyclic-noncyclic pair and its relevant new notion of coincidence quasi-best proximity points in a convex metric space. In this way we generalize the notion of coincidence-best proximity point already introduced by M. Gabeleh et al cite{Gabeleh}. It turns out that under some circumstances this new class of mappings contains the class of cyclic-noncyclic mappings ...

The functional inequality ‖f x 2f y 2f z ‖ ≤ ‖2f x/2 y z ‖ φ x, y, z x, y, z ∈ G is investigated, where G is a group divisible by 2, f : G→ X and φ : G3 → 0,∞ are mappings, and X is a Banach space. The main result of the paper states that the assumptions above together with 1 φ 2x,−x, 0 0 φ 0, x,−x x ∈ G and 2 limn→∞ 1/2 φ 2 1x, 2y, 2z 0, or limn→∞2φ x/2n−1, y/2, z/2 0 x, y, z ∈ G , imply that ...

The well-known Schwarz–Pick lemma states that any analytic mapping φ of the unit disk U into itself satisfies the inequality |φ′(z)| ≤ 1− |φ(z)| 2 1− |z|2 , z ∈ U. This estimate remains the same if we restrict ourselves to univalent mappings. The lower estimate is |φ′(z)| ≥ 0 generally or |φ′(z)| > 0 for univalent functions. To make the lower estimate nontrivial we consider univalent functions ...

In this paper, following [W.A. Kirk, P.S. Srinivasan, P. Veeramani, Fixed points for mappings satisfying cyclical contractive conditions, Fixed Point Theory. 4 (2003) 79-89], we give a fixed point result for cyclic weak φ-contractions on partial metric space. A Maia type fixed point theorem for cyclic weak φ-contractions is also given.