In this paper we study some fixed point theorems for self-mappings satisfying certain contraction principles on a convex complete metric space. In addition, we also improve and extend some very recently results in [9].

in this paper we introduce the concept of topological number for locally convex topological spaces and prove some of its properties. it gives some criterions to study locally convex topological spaces in a discrete approach.

We show that if $$(X,d)$$ is a metric space which admits consistent convex geodesic bicombing, then we can construct conical bicombing on $$CB(X)$$ , the hyperspace of nonempty, closed, bounded, and subsets $$X$$ (with Hausdorff metric). If normed or an $$\mathbb {R}$$ -tree, this same method produces . follow by examining nonempty compact assuming proper space.

Some fixed point convergence properties are proved for compact and demicompact maps acting over closed, bounded and convex subsets of a real Hilbert space. We also show that for a generalized nonexpansive mapping in a uniformly convex Banach space the Ishikawa iterates converge to a fixed point. Finally, a convergence type result is established for multivalued contractive mappings acting on clo...

M. Gromov [7] suggested to use coarse embeddings into a Hilbert space or into a uniformly convex space as a tool for solving some of the well-known problems. G. Yu [21] and G. Kasparov and G. Yu [11] have shown that this is indeed a very powerful tool. On the other hand, there exist separable metric spaces ([6] and [5, Section 6]) which are not coarsely embeddable into Hilbert spaces. In [9] (s...

and Applied Analysis 3 Lemma 3. Let p > 1 and E be a p-uniformly convex and smooth Banach space. Then, for each x, y ∈ E, φ p (x, y) ≥ c 0 󵄩󵄩󵄩󵄩x − y 󵄩󵄩󵄩󵄩 p (8) holds, where c 0 is maximum in Remark 2. Proof. Let x, y ∈ E. By Theorem 1, we have ‖x‖ p ≥ 󵄩󵄩󵄩󵄩y 󵄩󵄩󵄩󵄩 p + p⟨x − y, J p y⟩ + c 0 󵄩󵄩󵄩󵄩x − y 󵄩󵄩󵄩󵄩 p , (9) where c 0 is maximum in Remark 2. Hence, we get φ p (x, y) = ‖x‖ p − 󵄩󵄩󵄩󵄩y 󵄩󵄩󵄩󵄩 p − p...

in a fuzzy metric space (x;m; *), where * is a continuous t-norm,a locally fuzzy contraction mapping is de ned. it is proved that any locally fuzzy contraction mapping is a global fuzzy contractive. also, if f satis es the locally fuzzy contractivity condition then it satis es the global fuzzy contrac-tivity condition.

For a non-degenerate convex subset Y of the n-dimensional Euclidean space Rn , let K(Y ) be the family of all fuzzy sets of Rn , which are upper-semicontinuous, fuzzy convex and normal with compact supports contained in Y. We show that the space K(Y ) with the topology of endograph metric is homeomorphic to the Hilbert cube Q = [−1, 1] iff Y is compact; and the space K(Y ) is homeomorphic to {(...

In this paper, we introduce the (G-$psi$) contraction in a metric space by using a graph. Let $F,T$ be two multivalued mappings on $X.$ Among other things, we obtain a common fixed point of the mappings $F,T$ in the metric space $X$ endowed with a graph $G.$

In this paper we introduce the concept of generalized weakly contractiveness for a pair of multivalued mappings in a metric space. We then prove the existence of a common fixed point for such mappings in a complete metric space. Our result generalizes the corresponding results for single valued mappings proved by Zhang and Song [14], as well as those proved by D. Doric [4].