Existence of fixed point in orthogonal metric spaces has been initiated recently by Eshaghi and et al. [On orthogonal sets and Banach fixed Point theorem, Fixed Point Theory, in press]. In this paper, we introduce the notion of the strongly orthogonal sets and prove a genuine generalization of Banach' fixed point theorem and Walter's theorem. Also, we give an example showing that our main theor...

Let C be a compact convex subset of a Hausdorff topological vector space (E , τ) and σ another Hausdorff vector topology in E . We establish an approximate fixed point result for sequentially continuous maps f : (C , σ) → (C , τ). As application, we obtain the weakapproximate fixed point property for demicontinuous self-mapping weakly compact convex sets in general Banach spaces and use this to...

begin{abstract} in this paper, we introduce an iterative method for amenable semigroup of non expansive mappings and infinite family of non expansive mappings in the frame work of hilbert spaces. we prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality, which is the optimality condition for a minimization problem. the results present...

Some fixed point theorems and common fixed point theorem in Logarithmic convex structure areproved.

in this article, we apply two new fixed point theorems to investigate the existence of mild solutions for a nonlocal fractional cauchy problem with an integral initial condition in banach spaces.

motivated by samet et al. [nonlinear anal., 75(4) (2012), 2154-2165], we introduce the notions of $alpha$-$phi$-fuzzy contractive mapping and $beta$-$psi$-fuzzy contractive mapping and prove two theorems which ensure the existence and uniqueness of a fixed point for these two types of mappings. the presented theorems extend, generalize and improve the corresponding results given in the literature.

the aim of this paper is to prove a common fixed point theorem for nonexpansive type single valued mappings which include both continuous and discontinuous mappings by relaxing the condition of continuity by weak reciprocally continuous mapping. our result is generalize and extends the corresponding result of jhade et al. [p.k. jhade, a.s. saluja and r. kushwah, coincidence and fixed points of ...