where E∗ denotes the dual space of E and 〈·, ·〉 denotes the generalized duality pairing. If E∗ is strictly convex, then J is single valued. In the sequel, we will denote the single-value duality mapping by j. Let C be a nonempty closed convex subset of E. Recall that a self-mapping f : C → C is said to be a contraction if there exists a constant δ ∈ 0, 1 such that ∥f x − f y ∥∥ ≤ δ‖x − y‖, ∀x, ...

Zero point problems of the sum of two monotone mappings and fixed point problems of a strictly pseudocontractive mapping are investigated‎. ‎A strong convergence theorem for the common solutions of the problems is established in the framework of Hilbert spaces‎.

Suppose X = Lp (or Ip), p > 2, and K is a nonempty closed convex bounded subset of X. Suppose T: K —* K is a Lipschitzian strictly pseudo-contractive mapping of K into itself. Let {Cn}^_0 be a real sequence satisfying: (i) 0 < C„ < 1 for all n > 1, (") Z)rT=l Cn = °°> and Then the iteration process, zn G K, Zn+l = (1 — Cn)xn + CnTXn for n > 1, converges strongly to a fixed point of T in K.

‎in this paper, based on [a. razani, v. rako$check{c}$evi$acute{c}$ and z. goodarzi, nonself mappings in modular spaces and common fixed point theorems, cent. eur. j. math. 2 (2010) 357-366.] a fixed point theorem for non-self contraction mapping $t$ in the modular space $x_rho$ is presented. moreover, we study a new version of krasnoseleskii's fixed point theorem for $s+t$, where $t$ is a cont...

in this paper we investigate common xed point theorems for contraction mapping in fuzzy metric space introduced by gregori and sapena [v. gregori, a. sapena, on xed-point the- orems in fuzzy metric spaces, fuzzy sets and systems, 125 (2002), 245-252].

The purpose of this paper is to introduce an iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a k−strict pseudo-contraction non-self mapping in Hilbert space. By the viscosity approximation algorithms, under suitable conditions , some strong convergence theorems for approximating to this common elements are proved. Th...

In this paper,  we introduce the notion of  generalized multivalued  $F$- weak contraction and we prove some fixed point theorems related to introduced  contraction for multivalued mapping in complete metric spaces.  Our results extend and improve the results announced by many others with less hypothesis. Also, we give some illustrative examples.